You may not need to go to public lands. Last year hunting with shotguns shooting shot was allowed within the city limits in the daytime. You need to be at least 1/4 mile away from buildings to shoot. Open areas do NOT include areas within municipal parks, municipal preserves, county parks, county preserves, airports, golf courses, or posted water treatment facilities. Some areas within Phoenix are also closed.
I suggest going to the AZ Game and Fish Dept office (on Carefree Road about 2 miles west of I-17) and ask them about hunting coyotes on the south side of Carefree Road adjacent to the AGFD office. There is a large area across the street from the AGFD office that was just opened to hunting for the first time ever last summer and very few people know that area is now open. While you are there, you may need to get yourself a 4-day nonresident hunting license to hunt coyotes this week. Hunting coyotes near urban areas with a shotgun could be better than hunting on public lands anyway.
Good luck!