If your cousin and his wife have undergone conversion to Judaism by an Orthodox Jewish rabbi, then I cannot recommend handling this by seeking to argue Scripture with them. Here’s why:
Orthodox Jewish rabbis very rarely allow non-Jews to undergo conversion to Judaism; when they do so it is because they are satisfied that the potential convert has been educated thoroughly in Judaism, and will follow Jewish law completely and precisely. To assure themselves of this, Orthodox Jewish rabbis usually will not allow a potential convert to undergo conversion until he has already lived a Jewish life for quite some time (and even then the strictest of the rabbis will still hesitate to allow the formal conversion). In other words, what this means is that your cousin and his wife very likely not only know Scripture better than you do but are well-prepared to deflect the usual round of scriptural arguments Christians often lob in discussions with Jews.
What your cousin and his wife may not be prepared for is for you to greet the news of their conversion with unconditional love. If you greet the news of their conversion with sorrow for their choice but with love for them, you may well disarm their defenses. Ask them to describe their journey to Judaism, listen sympathetically, express admiration for their desire to search for truth. If they start attacking your faith by claiming that the Old Testament (which they likely will refer to as the Tanakh) does not support the messianic claims of Jesus of Nazareth, stop them and politely change the subject (e.g., “Let’s not talk about that right now, okay? Tell me more about [insert change of subject]”).
All the while, you might consider brushing up on your Catholic faith and how to defend it, so that when opportunities arise to speak positively about your faith you can do so. For example, one area in which modern Judaism’s lack of a developed theology causes questions to arise even for committed Jews is the problem of suffering. In the words of one Jewish convert to Catholicism though, Catholicism is in a real sense “a theology of suffering” because it has delved deeply into the question of what it means for God to have chosen to become man, to suffer and to die. If you have a solid understanding of the Church’s approach to the mystery of suffering, you may be able at some opportune time to help your cousin and his wife to see that the religion they left behind answers some of life’s toughest questions in a far more complete way than the religion they acquired.
