The thing is, it mostly depends on insulation. A well insulated room won't take much at all, whereas if that was previously a patio and doesn't have any insulation... good luck.
For instance, I have a 2.5 ton unit to do my basement. That would be considered grossly undersized by most people in Phoenix metro looking at cooling ~1500SF. But it's a basement in a block house... it's fine. In fact, it barely runs until it gets up north of 100.
I suspect, based on most of what I have seen of Arizona construction, especially on additions, is that you don't have much, so it's probably better to go big. That said... You can get a cheap 5000BTU unit for $150. A bigger one costs significantly more. And the little guy will probably do the job, even if it's running balls to the wall and it gets a little warm in the summer.
One other option are portables. I have one, nominally for my Garage, but it's damn useful if someone's AC goes out while it's being replaced. (In the garage, it's just to keep ME cool, it can't cool the whole 3 car garage and I don't try to)
ETA:
That portable I have is 7-8000 BTU. It did a damn reasonable job when my upstairs (also about 1500 SF) AC had issues last summer. It wasn't 'cool' but it at least kept the house liveable... and that's WAY outside what it 'should' be able to do. That said, it never had to do it for more than a couple hours before the main AC kicked back on. (Problem was a float switch that took a bit to run down. Previous owners had wired it to kill the thermostat if there was water in the pan. It would get humid, start to make water, back up, and kill the thermostat... but then it would drain and start back up. Removing the bush that had found the drain line was what fixed it.
)