The foxes live in the edges of the coyotes territory. Think of a territory as a large oval that is the coyotes home area. They will defend it from other coyotes as well. If you set any number of these "ovals on a map you would see where they overlap and have gaps. Those gaps are where the foxes live. They will go into the Coyotes territory, but usually when the coyote is on the farther end. Compared to the fox the coyotes territory is huge, he/she can't be everywhere at once.
Grey Fox have no difficulty as they can climb trees and coyotes can't. I find it hard to tell them apart in a B&W picture.