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?
You are misinformed. Coyotes are varmints in Idaho. No limits on shooting them at any time here.