I have had success in grilling rabbit, but yes, it can dry out in a flash. I guess I've been lucky as I don't use a thermometer on it as I find it's too bony to get a good 'read', but maybe that's just me. I brine my rabbit for about 4 hours.
I have also substituted rabbit in ersatz coq au vin, though I cut the marinade time down from overnight to a few hours since the pieces are so much smaller and less meaty than chicken.