If I have a coyote in my yard, I’m allowed to kill him or give my permission to someone else (like a friend or neighbor) to kill him, without a license, and any time of year. I consider alligators to be a nuisance the same way I do coyotes. They’re even worse than raccoons, groundhogs, deer, possums, and skunks.
Nuisance?
Only when tardos feed them. Otherwise they are shy creatures.