I am all in favor of coyote shooting - they're hard on deer, fawns, turkey, and out-compete foxes (I like foxes).
A few years ago I was in climber, hunting... I hear a deer. Readied... and out came a doe, moving at nervous walk, stopping... I didn't shoot, as it was rut, and I wanted something bigger. A minute later from same direction I hear crunch crunch crunch... oh boy, I'm thinking here come the big guy - raised rifle, and out comes a coyote, low-crawling... he was stalking the doe. Being a gentleman, I let her walk, and shot the coyote.