Do you think my cousin likes me?

From what you've said, it sounds like he does like you a little bit. Maybe he's not bold or stupid enough to come right out and say it. But I'd bet that if you came on to him really strong, he wouldn't reject you. I'm not going to lie. I have a female cousin whose a year younger than me and I had a bit of a crush on her when I was a teenager. I never acted on it because I knew it was wrong, but that didn't stop me from thinking she was attractive. She still calls me sometimes to ask my advise on things, and I'm glad to be there for her.