RE: hound for rabbits
I've been beagling about 16 years now and have never heard of a coonhound used for beagles. I do have 2 friends that double their deer dogs on deer/rabbits but it's a PITA when you're deer hunting and they strike a rabbit, we've got to shoot the rabbit to get them off it. You can only imagine what it's like when we're rabbit hunting and they strike a deer!
With that being said, I'd recommend a beagle if you're looking to strictly rabbit hunt. I don't know for sure, but I wouldn't think a coonhound could hold the trail of a cottontail too well, they'd want to push it too hard (which is what they're bred for) and you would have check (loss/breakdown) after check.