In areas in which shooting wolves or coyotes with rifles is legally impossible or socially impracticable, there is always the compound bow. Archery is one of those sports which has come several thousand years over the last 40.
compound bow is one option.
Sorry. Killing or injuring coyotes is illegal, in every state, as far as I know. I can’t even legally shoot coyotes or javelinas with a high powered BB gun - it could injure one of them. (Heaven forbid!)
Of course - if you have a deep hole dug and ready - who’s to know?