The Church does make provision for a Catholic whose spouse insists on using a contraceptive. Such a person is allowed, for the preservation of the marriage, to have intercourse so long as the other party uses the contraceptive. In the case you mention,
the wife would have to use a diaphragm, or pill, etc., since she is the one insisting on the use of a contraceptive.
Meanwhile the one who does not want to use contraception is urged to continue to try to educate the other to the teachings of the Church in this matter.
For documentation, see Vademecum for Confessors:
Fr. Vincent Serpa, O.P.