I know I'm late to this one, but anyway...
Here in Johannesburg, South Africa we've got Chinaberry absolutely everywhere. It's normally referred to as Syringa here, but that's an incorrect name. The Latin name of ours is Melia azedarach. I wonder if this is the same tree? Yellow, round berries. Bright green leaves.
I had to cut down a massive group of saplings in one section of my property (it was used as a hideout by some heavily armed burglars), and took the biggest stave I could find this afternoon. It's about 1 1/2" in diameter at the thin end and 66" long. I'm going to seal it and remove the bark tomorrow. It'll be the first bow I've ever attempted from a stave I cut myself!
Side note: How long do you think I should let it dry for? We have average max temperatures of 90(F), with sunshine all day, and a crazy low humidity.