The reward for running rabbits is--running rabbits. That's what beagles are meant for, tracking game. My beagles are well behaved dogs and don't bark and carry on in their kennels but when my hunting buddies show up they go crazy 'cause they know we are going hunting. Some people think you have to shoot the rabbits for them to stay interested and to reward them enough to keep them happy, not so. A good hunting beagle wants nothing more than a hot track to follow.
I've heard of lots of different methods of breaking beagles off of deer such as putting them in a barrel with a deer hide and deer legs then rolling it around until they are sick and such other methods. I can tell you that I broke a dog by holding him in a deer hide(hair towards the dog) and having my nephew hit the hide with a broom handle. It didn't hurt him but made such a loud noise it really scared the crap out of him, it was all I could do to keep him wrapped in the hide, he never ran deer again in his life even when other dogs hunting with him took off on deer. I tried that with 2 other dogs I owned and it had absolutely no effect on them, they weren't associating that with running deer tracks in the woods. I bought an E-collar and shocked them when they were running deer and they too became 100% deer broke. Not arguing with anybody but in my experience a shock collar is the fastest, most effective, and ultimately humane way to break a dog off of deer. I hunt in fairly wild country in Northern MI and if you allow your dogs to run deer you are taking a chance on losing them where they could end up freezing or coyote feed not to mention some people have been known to shoot dogs they see running deer.