If you are just making a run and put them away at night in secure area you could use chicken wire and t post. Coyote could still climb or dig under it prolly though. I just don't know how bad your problem is with coyotes and would the run be safe during the day.
Electric fencing will work in arid climate, but you need to be able to ground the system. You may be able to run a long grounding rod 6 to 8 foot in ground and hopefully get the rod into a moist subsoil.
You can try google and read about electric fencing in arid climates.
Also if you are in a...