AR_Clint,
I have a friend that has taken about sixty coyote's. He even makes distress calls for them. I don't know where he goes. But I suggest you get AZ Game & Fish 2003-2004 Hunt regulations book. Any Arizona Sportsman store will have them. Go to page #32 for General Predatory & Fur-bearing Mammals. This will give you all the info you need on where you can hunt statewide. Season is open year round. Also you must have hunting license. Hope this helps you.
PS. Take a pistol with you. My friend that I mentioned above had called one in. By the time he heard the coyote it was standing two feet behind him. So he used his pistol to kill it.
Also you can hunt on National Forest Land, BLM Land, and State Land. Just abide the hunting rules such as 1/4 mile from structures, no shooting over roadways or water and so forth.
And no hunting for them within city limits. Good Luck!