Air conditioning on a shoestring budget
Several thoughts, which could be used alone or in any combination:

1.) Have you thought of so-called "swamp coolers" (evaporative coolers)?

These devices work on the principle of evaporative cooling.  There are 2 basic types: Direct cooling and indirect cooling.  The direct cooling units are VERY simple and easy, but may result in air that is too humid to be comfortable (even though it is much cooler).  The indirect is more expensive and hard (but not nearly as expensive as conventional AC), and results in drier air.  Some systems use both methods: pre-cool the air via the indirect method, then run the cooled air through a direct cooler.  The result is cooler and drier air than either method alone.  All methods work best with very dry air (which it appears you have).

DIRECT method: Dry outside (or even inside) air is drawn through a wet screen or filter.  The cooled, moist air is pumped directly inside.  This method can be as simple as throwing a wet towel over a fan.  

INDIRECT method: Dry outside air runs through a wet screen or filter, to get cooled, and then across a heat exchanger which.  The dry air picks up moisture which cools the unit.  Inside air blown into the opposite chamber of the heat exchanger is cooled, but picks up no moisture.  Even this relatively complicated method is easier and very much cheaper to build (and operate) than an AC unit.  

2.) The simplest way to keep things cool is to deny the sun entrance.  

I had a home with a large skylight  in the kitchen.  Because I lived in a very temperate part of the northwestern U.S., I had no AC.  In the summer I would block off the skylight totally with a very light custom-cut board lined with aluminum foil; then take it down in the fall.  It made a huge difference (probably 5C in the kitchen).  

You could do something similar, using greenhouse shade cloth, chimney flashing, or many other items that run the gamut of the aesthetics/functionality tradeoff.

3.)  Venting the hottest air (from the top) and replacing it with cooler air will help; or you could leave that air alone and recirc the cooler lower air, to make it even cooler.  In either case, forcing the air through deeply buried pipes would cool it.

The temperature of the earth, almost anywhere on Earth you would want to live, is roughly in the neighborhood of 50F (10C).  You just have to dig down deep enough to access that temperature.  All the desert critters know this: that is why they stay underground during the day.  Even if you only want to go down two meters, you should be able to access constant temperatures of lower than 15C.  Then you bury some pipes and force the air through them.  The air heats the dirt, but that dirt is cooled by the surrounding dirt.  Basically you are using mother earth as a heat sink.