I might say, puzzled, "You're not serious, right?"
And then, "you know, people have been making that joke all my life--frankly it's annoying. I'd like to ask you to never make it again, yourself, and to do what you can to influence other people to stop.
"Even if you think you're joking, it makes me look like a petty, small-hearted person. And that's really unfair to me.
"Also, I would hope my cousin knows that it's YOUR joke and not mine, but if she hears it, she may feel really awkward around me.
"Please, can you help me get people to stop? If they think they need to say something, they can say, 'How neat that you two have so much in common!' "
The reason I vote going for the longer explanation is that these are people who are around awhile, and a longer explanation is worth the investment.