My favorite cooking method for rabbit is BBQ cooking. Grilled rabbit or barbecued is great, and my favorite piece is the backstrap, or loin. If your rabbit is young, the meat will likely be pretty tender. If the rabbit is older, you might want to parboil it before grilling.
Just as there are several ways to dress a rabbit, there are lots of rabbit recipes for BBQ cooking. Some people like to soak the meat overnight in salted water. I usually prefer to use a wet rub on the meat, much the same as I would with pork or chicken. I use olive oil, cider vinegar, salt, black pepper, ground red pepper, onion powder, and garlic. Form the mixture into a paste and rub the rabbit all over. Place the meat in a bowl, cover it, and leave it in the fridge for several hours.
Preheat your grill to around 300 degrees, or use the indirect cooking method over charcoal. Make sure your grate is clean and oiled. After the rabbit has cooked for about 45 minutes, start brushing it with your favorite barbecue sauce. Rabbit should be done in about another 15 minutes. At this point, I like to dunk the pieces of meat in the bbq sauce and cook them over high heat for a couple of minutes to caramelize the sauce.