How to barbecue marinated chicken drumsticks
Alton Brown has an interesting technique in an episode of Good Eats in quite a bit of detail.

But, what I just do is to put it on direct heat (right over a medium-high flame) to sear the skin side and then move to indirect heat (burner right below turned off, other burner still on) and cover to complete. I will admit I've burned it a couple times, but every time I do, it's cause I've forgotten to check it, and left it without checking it.