I live in AZ and wanted to chime in.

You can find big Coues in just about every southern unit in AZ. With the exception of archery, you have to put in for a drawing to get a tag. Early season (October) and middle season (late November to early December) are easy to get drawn for; being a non-resident there are no sure things on getting drawn the first year. Late season (last couple of weeks of December) can be extremely difficult to get drawn for; even harder for non-residents. The old saying "you have to be in it to win it" does apply.

Having quality optics (ex: Swarovski SLC 15s) with a tripod for day-long glassing sessions, being able to hit a very small target at extended ranges, be prepared for significant temp changes in the same day, quality boots (sucks to have cactus spines go through your boot soles), and a ton of patience can help lead to a successful hunt. Unlike TX there is plenty of public land in AZ to hunt. Also grab a mountain lion tag since you never know when you'll come across one and there are plenty here in AZ.

If your glassing skills are non-existent or minimal, I would strongly recommend doing a guided hunt the first time out. It'll make things much easier and can shorten the learning curve on hunting them. Coues are called the "grey ghost" for a reason; they are hard to find and can disappear in a blink of an eye. I just got back from a Coues hunt in Sonora MX and hunted with eight other hunters who each have literally successfully hunted the world. Despite their experience, every single one had issues finding deer (their optics were not sufficient), had troubles seeing them in our SLC 15s (on a tripod with the head locked with the deer in the middle of the field of view), and had a nightmare of time finding them in their rifle scopes (we set their rifles up for them prone with the crosshairs on the deer). Thankfully everyone got a buck but is was extremely challenging. If they had done this unguided in AZ, it is highly unlikely any of them would have harvested a Coues buck.

I do suggest hunting them but go in with realistic expectations. Do be prepared to get your butt kicked by a 90 pound critter while enjoying every moment of it. You'll see some amazing country as well. They are extremely addicting to hunt. If you want an outfitter suggestion I can give you one.