Hardin, I've hunted deer and elk in Unit 9 and I saw coyotes in just about every outing that I can recall. Although I didn't specifically hunt coyotes, I'm sure both Units 9 and 7 would serve you well. I've done a little coyote calling in Unit 7E, with decent results. Get nearer the Navajo Reservation boundary for best results.
The only downside is the heavy population of Flagstaff and the probable hunting pressure from varmint hunters who live there. I'd give it a crack this coming September - if'n I were you.
Hunting can be slow and frustrating if Mother Nature throws a warm hunting season at you. But things can take a drastic turn for the better with the onset of a cold snap. Whether you get snow or just a good, prolonged cold front, the hunting can improve on a dime. But cold whether can also make certain parts of the hunt more tedious. Here are some things to keep in mind when your prayers for cold weather finally pay off.
You can see a your quarry's breath when it is cold outside...