Just talk to him. Try to be his best friend.. shit.. but don't mention his depressing stuff in the beginning... Just be there for him.
I went through something like that exactly when I was 14... Well.. maybe not wanting to kill people, but I did listen to some dark death metal and black metal and was reading satanist bullshit online... So you can make an idea.
My family stuck close to me and my uncle especially... and now I'm absolutely fine
So if you want to help your cousin, forcing him to get "help" is not the way to go. Just spend more time with him, be his "idol"

You're older than him I reckon. How old are u?