It sounds like a challenge from a reality show: design a desert garden that can survive without irrigation. Obviously you need to use low-water plants. (Native plants make sense.) Utilize the runoff from your roof to provide water for your desert garden. You can sculpt berms and basins to guide the flow of water around your planting area. Plant in fall or winter to give everything a chance to get established before the heat hits. The first year or two you can water by hand with a hose to supplement the rain. My yard has areas on a drip system and areas off–it is interesting to experiment and see how the plants fare (once you are confident enough that you won’t kill them!).
Here are some plant choices suggested by Scott Calhoun:
Next to a basin
Ironwood, Western Soapberry, Desert Hackberry. I would add Foothills Palo Verde.
Baja fairy duster and pink fairy duster, Bee bush, Chiltepin, Desert honeysuckle, Desert lavender, Globemallow, Southwest coral bean
Desert milkweed, Prairie zinnia, Sundrops, Trixis
Almost all cacti and agaves do well above a basin where their roots won’t ever sit in the water.
In a basin
Desert willow, Velvet mesquite
Apache plume, Arizona wild cotton, Limber bush, Mariola, Oreganillo, Wolfberry, Shrubby senna, Tarbush, Yellow bells
Deer grass, Flattop buckwheat, Goodding’s verbenia, Penstemon, Sacred datura, Wright’s goldenrod.