I can deeply emphasize with your cousin’s situation and admire you desire to help. But paying for therapy isn’t the answer because he isn’t ready. This type of concomitant issue — with depression and narcotics, is very difficult to break and unless the person is motivated himself the therapy and recovery process doesn’t work.
I know this is very hard to watch, but the best thing you can do at 16 years old is let him know you care, believe he will find a way to deal with it when he is ready, and can be there to support him emotionally. There are plenty of free programs available (not the least of which is narcotics anonymous and if there is Alcoholics Anonymous. Your job is to get some support for yourself from free organizations like Nar-Anon, Al-Anon and Al-Ateen. Finally, I would strongly suggest not giving him money for therapy as the money typically gets used for drugs and not therapy. Your cousin has to want to turn his life around — and until he does the most important thing you can do is have compassion.
Wishing you patience and peace,
Proof Positive Blog @ PsychCentral