My wife is a non-Catholic who has threatened me with divorce if I don’t get a vasectomy. She refuses to practice, or even consider Natural Family Planning. I am unwilling to get a vasectomy but I’m willing to abstain altogether---which would be difficult

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.

When one spouse does not wish to practice birth control, but the other insists upon it, the Church allows the non-practicing spouse to engage in relations with the contracepting spouse for the sake of maintaining the marriage. The non-practicing partner is not allowed to use birth control himself, he must make his opposition to birth control known, and -- at appropriate times -- he should seek to educate his spouse about the morality of the practice. But, he can tolerate the fact that a contracepting spouse insists on birth control. In this case, you cannot agree to have a vasectomy, but you can engage in relations with your wife even if she insists on using birth control herself.

Source: Vademecum for Confessors Concerning Some Aspects of the Morality of Conjugal Life by the Pontifical Council for the Family