Bring in some eagles to hunt down the rabbits. Only danger they pose to cars is if they poop on them. Of course, they might try to carry off a small child or pet dog, but that’s when you bring in the poison gorillas to get the eagle problem under control - according to the Simpsons, anyway.
Eagles (other than the F-15 variety) are probably not a good idea around an airport. Wolves or coyotes, maybe even foxes? Of course, you start with bunnies and foxes around the airport and the jokes will be non-stop.