I assume fresh rabbit as opposed to wild. If wild you'll need to brine either in milk, buttermilk, or salt water to clean out some of the gaminess. It is extremely lean, in the wild you can actually die from rabbit because its so lean, the trappers used to eat grass with the rabbits.
In the south we usually fry it (you're shocked right?), the usually Cajun type fare like jambalaya, gumbo, fricassee and I do love it smothered.
I would think a brine would be suitable. In the past smoking we always smoked the rabbits to be used in other type dishes as above.
BTW I have two rabbits sitting in milk right now, I cried, I forgot them and they are a little freezer burned. I am fixing to do jerky after a tenderloin today, corned beef pastrami tomorrow, so will probably be Tuesday....LOL But these were shot out back. They were real gamey when I froze 'em.
As to your smoke, I would go with a fruit brine approach, then compliment with the wood, peach wood/peach brine, cherry wood/cherry brine, apple, etc. I always do very low and slow.
BTW if it want it splayed out, then spit it before smoking. Mine always wanted to end up in the fetal position.
I just noticed I was more BS than help, Sorry.
