How do you make a teenager happy??

I have a moody teenage boy in my house. Some days are great & we have lot of fun. Some days are sad & I want to cry for him. Most days are just ugh! There seems to be no way to make him happy.
When I got married he was not happy about it. he was determined to hate his new step father, even though prior to us getting married he thought he was great! When we moved he was determined to hate Florida too. Now, he still isn't too happy with his step-father (5 years later), but he doesn't want to leave Florida. When I told him I was pregnant he was FURIOUS, now he loves his baby sister. Everything about this boy is contradictory. He wants to keep his dog, but doesn't want her in his room or want to clean up after her. He wants an allowance, but doesn't want to do his chores 100% in order to get it. If I give him and hour to play on the PS3 he wants 4 more. If I say he can go out before dinner, he wants to go during dinner.
I know it's pretty typical teenage stuff, and for the most part I am not worried. Every once in a while, though, I'd like to see him happy. Genuinely. Happy.
I just don't know how to do it.