I understand that the Church teaches that under certain circumstances a Catholic may engage in marital relations with a spouse who contracepts (so long as the non-contracepting spouse is attempting to dissuade the other and has informed the contracepting spouse of his moral stance). I am wondering, however, whether a Catholic is still required to consent to marital relations even if his spouse uses contraception. Or may he choose to deny his spouse marital relations in such a situation?
Ordinarily speaking, spouses have a right to marital relations that they receive when they enter into matrimony with each other. Such a right must be exercised with mutual respect and prudence, and may be deferred for just reason.
In theory, it does appear that a Catholic may say no to marital relations with a contracepting spouse because the contracepting partner is engaging in activity that both sterilizes the marital act, and, to a certain extent, abuses the marital relationship by treating his or her spouse as an object to satisfy personal pleasure rather than a sacramental partner with God in openness to new life and to total union with God and each other. That said, there is a question of whether or not absolutely denying marital relations to a contracepting spouse would be a prudent thing to do.
Marital relations are very important to the spousal relationship, to such an extent that the Church ordinarily treads very lightly when giving pastoral counsel in this area. One of the reasons that the Church tells Catholics that they may tolerate contracepting spouses so long as they do not contracept themselves is because the Church is trying to help Catholics to preserve their marriages. In the past, absolutely denying marital relations when one of the spouses was contracepting might have been possible because divorce was so difficult to obtain. In a society in which there is access to easy divorce, the denial of marital relations might be more likely to lead to divorce than to the conversion of the contraceptor. To avoid the great evil of divorce wherever possible, lesser evils may sometimes be tolerated when there is proportionate reason to do so.
You can read more about this in the Vademecum for Confessors by the Pontifical Council for the Family.