Trap the Rabbit to Kill It
Live trapping to transport rabbits to distant habitat is not recommended. Aside from the fact that it is illegal in many states to transport wildlife without a permit, the issue is the impact on the rabbit after it has been freed into a new territory. It is usually destined to cause overpopulation in a territory already sufficiently populated for the available food supply. So the newcomer creates stress among the existing rabbit population, even possibly introducing disease. Very likely you transfer the rabbit problem to some other nearby homeowner.
However, appropriate live traps for rabbits are commercially available as humane alternatives to traditional leg holds. The idea is to humanely capture the animal so that he can then be humanely killed. Use a box trap measuring 10 by 12 by 30 inches. Because rabbits are more likely to enter a dark trap than a well lighted one, cover it with a tarpaulin.
Baits For Trapping Rabbits - The best baits will vary from winter to summer when rabbits foods are more available. Good winter baits to try include bread, corn on the cob, dried apples, alfalfa, and clover. Successful warm weather baits include fresh vegetables (carrots, lettuce, cabbage, brussels sprouts) and apples.
Once it is trapped the animal is your responsibility. You must dispatch it by some means, usually shooting (where discharge of firearms is permitted), asphyxiation or drowning. If you do not want this responsibility, do not use a trap. Deal with rabbits in some other way. Perhaps you call you local Animal Control official.
Encourage the Predators
Encourage the Predators of the Rabbit
Rabbits have many natural enemies, which may help you in your battle to rid the yard of these persistent pests, or at least keep their numbers down to a reasonable level. Certain snakes of the genus Pituophis (bull snakes, gopher snakes, and pine snakes) are fond of baby rabbits. Other predators include cats, dogs, king snakes, barn owls, weasels, foxes, hawks, raccoons, and coyotes. You scoff at coyotes. That critter is all over the place. In New Jersey they estimate the coyote population at over 2500. Those critters eat a bunch of rabbits.