A few seasons ago I had a coyote come trotting into my decoy shortly after sunrise on a windy day. He got suspicious at about 30 yards and I unloaded into his face. He rolled over, got up and ran off like he'd never even been hit.
I thought the set-up was blown but it was too late to move, so I decided to get really aggressive. Surprisingly, a tom hit on my cutting and ending up coming in and did not survive a 30 yard shot of his own.
Time and time again, I see evidence that a shotgun blast means little to a turkey. I do not suggest that you shoot every coyote, but if you have decided they need to be thinned, I would not hesitate.