Contacting the cousin is the best answer.

Only you can answer this question, but since you "live in sin" as you put it, do you think your mother is so urgent for him to come so she can make a scene in front of the rest of your family about your cohabitation status? If that's not the case, I don't understand why you would feel so uncomfortable? It's not like they have to find out you live together just because he came with you, do they?