Formal cooperation occurs when the act of the other person is intrinsically evil, and the cooperating act is ordered, by the nature of the act, to assist in attaining the evil end of that intrinsically evil act. This makes the cooperating act also intrinsically evil. Therefore, formal cooperation is always morally illicit.
A husband knows that his wife is using abortifacient contraception. He cannot have marital relations with her, in that case, because his act of having relations with her is directly related to the very nature of her sin. She cannot accomplish the sins of contraception and abortion without his cooperation. Moreover, in the circumstances of the act, he can stop a prenatal from being killed in the womb by the abortifacient, by merely refraining from sex. The loss of human life far outweighs the loss of sexual relations, so the font of circumstances also requires him to refrain.
A similar analysis applies if the husband wishes to use a condom, and the wife must decide whether it is moral to have marital relations that is contracepted by that device. The use of condoms is intrinsically evil, as it is a type of contraception. Her cooperation is directly related to that use, since without sexual relations the contraceptive act cannot occur, and it is the very act of sex which she is deciding upon that is harmed by the contraception. So she cannot morally have sex with her husband, if he is using a condom.
The only separate case would be the use of the method of contraception called withdrawal by the husband. The wife begins by having natural marital relations, and the act is not, at that point in time, contracepted. It is only when the husband withdraw that the sin occurs, and she is not part of that act. So, for a grave reason, and if she has many times attempted to dissuade him, she may consent to marital relations. I should point out, though, that most of the time the wife will not have a grave reason, and so she should usually refuse.
Denzinger  has a decision of the Holy See on this topic. It is quite clear:
“Question: Can a woman cooperate legitimately in an action of her husband who, in order to indulge his lust, wants to commit the crime of Onan or the Sodomites and threatens her with death or other grave injury if she does not submit?
“Response: a. If the husband wants to commit the crime of Onan in the marital act, that is, by expelling his seed outside of the vagina after the initiation of copulation; and he threatens his wife with death or other serious injuries if she does not agree with his perverse will, the wife, according to approved theologians, can, in such a case, join herself sexually to her husband since, on her part, she engages in a legitimate object and act, but she permits the sin of her husband for a grave reason, which excuses her: since charity, which would require the prevention of the act, does not oblige in the face of such peril.
“b. If, however, the husband wishes to commit the crime of the Sodomites with her, since Sodomitic intercourse is against nature on the part of both spouses who are united in this way, and, in the judgment of all the learned teachers, is gravely evil, there is clearly not motive, not even to avoid death, that would permit the wife legitimately to carry out such a shameless act with her husband.” [Denzinger 3634, in its entirety]
Discussion: The crime of Onan can be taken as contraception, or as masturbation. In the former case, the act of Onan is literal, and in the latter case, it is extended to include similar acts, such as solitary sex. In the above passage, the sin at issue is contraception. But notice that the wife can only cooperate on two grounds. First, the act on her part must be entirely moral, natural marital relations open to life — at least, it is open to life until the husband, on his own, withdraws. So, while she is participating, the act is natural. Second, she nevertheless can only participate for a grave reason, such as threat of violence, or, in other cases, threat of divorce which would cause grave harm to the lives of the children, or the likelihood of adultery. But the wife may not ordinarily cooperation with even the sin of withdrawal.
Elsewhere, as will be shown below, the wife may never cooperation with sexual acts that are contracepted from the beginning, such as the use of condoms. And this certainly implies that the husband may not cooperate with the worse sin of the use of abortifacient contraception by his wife.
As for the crime of the Sodomites, notice that the text allows no exception. The act is intrinsically evil from its beginning. A subsequent withdrawal without climax, followed by the natural act does not make the previous actions moral. Sodomy is a shameless act which is against nature, and it does not become moral by the lack of climax, nor by a subsequent natural marital act.
Denzinger [3638-40] also had a response of the Holy See on artificial contraception:
“Questions: 1. Is a wife, when her husband wishes to practice onanism by means of an (artificial) instrument, required to exercise positive resistance?
“2. If the answer is negative, could the woman honestly exercise passive resistance for reasons equally serious as those that pertain to natural onanism (without an artificial instrument), or, rather, are the most grave reasons absolutely necessary?
“3. So that this entire matter might be developed and taught in a more certain way, must a man, using such instruments, truly be regarded as equivalent to an aggressor toward whom the wife must offer the same resistance as a virgin would toward a rapist?
“Response: to 1. Yes. — To 2. Provided for in the first. — To 3. Yes.”
Note that the word “honestly” above is better translated from the Latin as “justly”, “uprightly”, “properly”, or “reasonably”.
Natural onanism is contraception by natural means, i.e. withdrawal. Artificial onanism is contraception by artificial means, such as a condom, a female barrier method, an IUD, or chemical contraceptives. The artificial version of the sin is worse, since it is further from the moral natural act. Also, any contraceptive method which is also an abortifacient is much more gravely immoral, as innocent human life is lost.
We can apply the above teaching of the Holy See to other sins. The crime of Onan is not only contraception, but also, by extension, masturbation. And so, masturbation with an instrument (sex toys) is more gravely disordered than without; though both are mortal sins. Now the Sacrament of holy Matrimony was not established by Christ in order to justify gravely immoral sexual acts. Contraception does not become moral when done within marriage. Neither does any intrinsically evil sexual sin become moral within marriage. So the crime of Onan as masturbation does not become moral when done by one spouse on the other. And such a crime is worse when performed using an artificial instrument, just as contraception is worse using an artificial instrument. For the wife can, under grave duress cooperation with natural onanism, but not artificial onanism. Can she then cooperation with masturbation when that act is not done with an instrument? No. The act is intrinsically evil from its beginning, just as sodomy is.
Another passage of Denzinger , quoting a decision of the Holy See, also discusses contraception.
“Questions: 1. Is the imperfect use of marriage licit, whether it happens by onanism or ‘condomistically’ (that is, by using the abominable instrument commonly called ‘the condom’)?
“2. Can the wife, aware of such ‘condomistic’ union, yield herself passively?
“Response: (decree of April 6, published April 19, 1853): To 1. No, indeed, it is intrinsically evil. To 2. No, she would indeed be engaging in an act that is intrinsically illicit.”
Since the act of the husband is intrinsically evil from its beginning, the wife cannot cooperation or she sins gravely. The same analysis applies to the crime of the Sodomites: the act is intrinsically evil from its beginning, and therefore it cannot be used as a type of foreplay.
The husband may not have marital relations with his wife, if she is using any form of contraception or abortifacients. And the wife may not have marital relations with her husband, if he is using condoms or any other form of contraception. (For we know that male chemical contraceptives are under development.)
Unfaithful Catholics are currently using the internet to spread many different types of errors, especially ones that justify contraception in various cases, and justify unnatural sexual act sin marriage. Proponents of the error that a spouse may cooperate with condom use or abortifacients usually cite the Vademecum. But that document explicitly condemns cooperation when the act in question is intrinsically evil. And of course, the use of contraception or abortifacients is intrinsically evil. What the Vademecum permits, only for a grave reason, is exactly what is permitted by the Holy See in the above quote about natural onanism (withdrawal).
The Vademecum (guide for confessors) states the following:
“4. The Church has always taught the intrinsic evil of contraception, that is, of every marital act intentionally rendered unfruitful. This teaching is to be held as definitive and irreformable. Contraception is gravely opposed to marital chastity; it is contrary to the good of the transmission of life (the procreative aspect of matrimony), and to the reciprocal self-giving of the spouses (the unitive aspect of matrimony); it harms true love and denies the sovereign role of God in the transmission of human life.”
Contraception is intrinsically evil and always gravely immoral. The assertion that the Church has “always” condemned this act, and that the teaching is “definitive and irreformable” implies that the condemnation of contraception is intrinsically evil under the ordinary and universal Magisterium.
“5. A specific and more serious moral evil is present in the use of means which have an abortive effect, impeding the implantation of the embryo which has just been fertilized or even causing its expulsion in an early stage of pregnancy.”
The use of abortifacient contraception is more gravely immoral, as it has an abortive effect. Note that some present-day theologians are now claiming that abortifacient contraception is a less serious moral evil, and that mere barrier methods such as a condom are the more serious evil.
“13. Special difficulties are presented by cases of cooperation in the sin of a spouse who voluntarily renders the unitive act infecund. In the first place, it is necessary to distinguish cooperation in the proper sense, from violence or unjust imposition on the part of one of the spouses, which the other spouse in fact cannot resist.46, 561).] This cooperation can be licit when the three following conditions are jointly met:
* when the action of the cooperating spouse is not already illicit in itself; 
* when proportionally grave reasons exist for cooperating in the sin of the other spouse;
* when one is seeking to help the other spouse to desist from such conduct (patiently, with prayer, charity and dialogue; although not necessarily in that moment, nor on every single occasion).
“14. Furthermore, it is necessary to carefully evaluate the question of cooperation in evil when recourse is made to means which can have an abortifacient effect. ”
Footnote  references Denz. 2795, 3634. Therefore, the Vademecum may not be used to contradict the teaching of the Holy See in those passages from Denzinger. For then the action of the cooperating spouse is illicit in itself, i.e. it is intrinsically evil. So the commentators who cite the Vademecum to support their claim that one spouse can cooperation with the other using artificial contraception teach a grave error, which harms souls and, when abortifacient contraception is at issue, also kills prenatal human life.
Footnotes  states the following:
“From the moral standpoint, it is never licit to cooperate formally in evil. Such cooperation occurs when an action, either by its very nature or by the form it takes in a concrete situation, can be defined as a direct participation in an act against innocent human life or a sharing in the immoral intention of the person committing it” (John Paul II, Enc. Evangelium Vitae, March 25, 1995, n. 74).
Therefore, cooperation with a spouse who is using abortifacient contraception is “never licit” as to do so is “to cooperate formally in evil”. In the case of abortifacient contraception, the cooperation is “by its very nature”, since, as the Holy See teaches above, the use of any form of contraception is intrinsically evil, and, as the Vademecum states (n. 5), the use of abortifacients is even more gravely immoral.
So, then, there is no legitimate reason for any Catholic to teach or to claim that one spouse may cooperate with the other by marital relations when their spouse is using contraception or abortifacients. The spread of this error online is doing grave harm to body and soul.
Please take a look at this list of my books and booklets, and see if any topic interests you.