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.
A perk of majoring in wildlife biology in college is the plethora of hunting knowledge that you collect throughout your course load. One of the most important factors in whether an area can hold large quantities of animals or produce large antlers is forage.
Most universities, state schools and even community colleges offer basic botany courses and plant ID courses. Although it might not be feasable for the average middle age hunter to pay tuition and go back to college to learn hunting...