As a kid I had success hunting rabbits without beagles. By the time I was 18 I had them. Have'nt hunted without them sense. To find one without a dog snow is a key, but if no snow you have to atleast find an area that holds rabbits. Thickest nastiest area possible. If you sneek through it you may see one sitting. look everywhere and pick apart everything. You will usually pick out that little black eye looking at you.
Plan B: pound the brush and be your own dog. Kick every log, briar bush, and jump on every brushpile. Be ready for a fast shot. Did I mention snow helps? Snow will make a moving rabbit look like an easy to see target. Snow will also narrow down areas to check.
Plan C: Find someone near you with dogs. I know it sounds weird but it could work.I know if I ran into another BP hunter in my area and they wanted to come along I would gladly allow them. Hunting over dogs is different though. With dogs you will get more rabbits usually, but its more about working the dogs than just killing bunnies. Not that I would have a problem with you jump shooting a bunny while we were working my dog, but many guys would.