CFG, you made a very good point about shotguns versus BBs versus a rifle. Thanks for clearing that up, I appreciate it.
Shooting rabbits with a shotgun may not be an option for those looking for a permanent solution
because rabbits breed, making them a rock that has to be freshly rolled up the hill every morning. Shooting them is definitely not an answer for those in communities where laws restrict the use of firearms in a public space. Always check with your local law enforcement before attempting something like this so that you do not break your local laws.
A possible natural solution
As far as a solution that works with nature and requires less effort on a homeowner's part in Kentucky
, have you considered installing a barn owl nest? Barn owls are nocturnal predators that eat baby rabbits and other small rodents. You may want to contact the Kentucky Department of Fish and Wildlife to see if this is a viable solution where you live. The links I have posted below contain contact information.
Below is some information I found and since it's from a U.S. government site and thus free of copyright restrictions, I have quoted extensively from it. Here is some information I found:
[url=https://fw.ky.gov/navigation.aspx?cid=631&NavPath=C100C366]The Disappearing Barn Owl
Providing nests can help restore their numbers
Barn owls, with their distinctive heart-shaped faces and dark eyes, were plentiful across Kentucky as late as the 1960s. However, biologists are concerned about current low barn owl numbers as the nesting sites and hunting grounds of these birds have disappeared.
...Barn owls have gradually lost their nesting and foraging habitat as landowners cut down the old trees damaged by storms and converted pastures, hayfields and grasslands to row crops. Pesticides and competition with other owl species also may have contributed to their decline.
These birds do not construct nests. They prefer to lay their eggs on a flat surface well above ground level, such as a shelf. They lay five to seven white, often nest-stained eggs, which the female incubates for 30-34 days. Juvenile owls are ready to leave the nest about 8-10 weeks after hatching.
The willingness of barn owls to use man-made structures means artificial nest boxes put into areas with the right habitat can boost the numbers of these birds. Employees of the Kentucky Department of Fish and Wildlife are already placing nest boxes inside existing buildings on wildlife management areas with suitable barn owl habitat. The department also encourages landowners that have suitable habitat and buildings to take advantage of the opportunity to provide nest sites on their property.
If you follow the link below it will show you how to construct an artificial nest to encourage barn owls on your property.
[url=https://fw.ky.gov/pdf/barnowlboxes2010.pdf]Barn Owl Nest Box Assembly and Installation
The barn owl is a nocturnal species which occurs in open habitats where it preys on rodents and other small mammals. Although they are one of the most widely distributed birds in the world (found on all continents except for Antarctica), they are listed as a species of greatest conservation need in KentuckyÃ¢â‚¬â„¢s State Wildlife Action Plan, due to local decline. Nest site availability is a major limiting factor for barn owl populations and providing nest boxes to barn owls has been found to successfully increase populations.