I recently smoked four rabbits, and they turned out really good. Here is what I did.
I cut four rabbits up into pieces, just like a chicken. I then soaked the rabbit in brine for 2 1/2 hours. Here is the brine ingredients.
6 cups water
1 cup fresh basil, chopped
1/3 cup oregano
6 tbsp salt
2 tbsp sugar
6 tbsp crushed garlic
1/3 cup red wine vinegar
1 tbsp red pepper flakes
After soaking in brine for 2 1/2 hours, pat meat dry with towel. Lay the pieces of meat on your smoker racks, evenly. Smoke-cook for 2-2 1/2 hours at 240 degrees.(The front legs can come out at 2 hours) I used about 2 oz of cherry wood with mine, but choice of wood is yours.