Very few coyotes around here but one of ours would chase fox off all the time. Don't think that predators like to mess with cats in good health much. Too much effort and risk for the meal.
Funny too that sometimes they'd kind of play together... Fox would sit off a little and get down on its front haunches and bounce back and forth like a dog trying to get the cat to play with it. Cat would make a move and it would run off a little and stop and do the same thing again. Sometimes it would make a move and the cat would run off and turn around and come back and do the same. Back and forth like that. They'd get a lot closer than you'd think. Sometimes just sit there together hanging out for a long time.