I used to trap until the anti-fur PETA people messed it up. Trapping was well managed and helped control the population with no threat to the environment. Now they are out of hand and need to be shot. It was dumb, same final end result anyways.
FWIW, coyotes were unknown in rural Pennsylvania just a decade or so ago. Now, they are just starting to be a real nuisance! I’ll bet some damn PETA type introduced them.