What trees do you see around your area that handle the climate and dry conditions? Those would probably be the best bet. I know that people often complain about oleanders, but you can prune it to a tree shape, it is rather bushy (for privacy) and definitely showy when blooming. Plus it's evergreen and can take droughty conditions better than other potted trees/shrubs.

Hi Dunny
Ficus are good potted trees.They like the sun. I have two. Since its cold here I bring them in during the winter. My largest is 7 ft. They can get bigger if the container is big enough.

The toughest I can think of would be variegated privet.

They are tolerant to sun or shade and heat or cold. Also drought tolerant in the ground. They are evergreen and smell very sweet in the Spring.

I have one in the yard that I have trimmed into a tree for 10 years. It is 12 feet tall. I'm getting ready to put one in a pot on my shady but hot patio. They grow quickly so don't be disturbed that it doesn't look like a tree. Just take out your clippers and trim it into a tree.