cousin's wife

There, you said it. That is the problem. Your cousin, aka her husband, gave his wife your contact info and told her to become your friend. Perhaps she is doing just that and trying to be an obedient wife. I don't think she is the annoying one. I think its your cousin who gave your personal info to her without consulting you first.
You said he was "thrilled" after she contacted you. Don't you think he told his wife that he gets happy when she communicates with you? Its not her fault. She is just trying to make her hubby happy.