I told my cousin he's adopted
Why do you think he's adopted?
Because his parents are too good to him.
It is wrong to lie to someone to make them feel bad. You should get some professional help to deal with your jealousy.
I don't like how shy he acts. He should be more confident and standing up for himself.
Instead of lying to him about his parents, why don't you work with him to help improve his confidence. Lying to him about his parents will only make him feel more insecure, but if you can support him, I'm sure he'll blossom in no time.