I also live in Arizona, about halfway between Phoenix and Flagstaff. I have a 10x15 run that I built out of a modular dog run (it's made of panels, with the fabric already on them), and a shelter/roost taking up a corner. I used hardware cloth around the bottom 4 ft, an apron around the perimeter, and 2x4 no climb for the top, with hardware cloth near the roost. And lots of shade cloth as I have no trees yet. Where I live, the coyotes breed in January with kits in March but your area could vary. Best of luck!