I use a .50 caliber when I hunt them nasty little red pinr squirrels. They like to get into buildings and tear everything up. I was shooting them with a Hawkins, using 70 grains and a round ball. I was not fussy where I hit them as long as I hit them. I knew with that load it was accurate. In my scoped .50 caliber Wolverine, I shoot 50 grains and a patched roundball and that is an excellent and accurate small game load.

With almost any black powder weapon, and rabbits, you still have to do a head or front end shot to save the meat on the hind legs at least. Or take them low in the belly and you can field dress them at the same time (done that with a .54 caliber once). They say that tradition's Crockett rifle is a nice rifle but I do not own one. I hunt rabbits with a black powder revolver now in .44 caliber. I don't hit many which is fine with me too...

Another option might be a black powder shotgun. Then you can hunt rabbits, squirrels, birds, even turkeys...