A stand up mister (that you screw onto your hose) was $15 at Walmart or Homedepot. We got tubing, T's, and sprayer heads for about the same, but it can stretch like 40 feet. You could run that sucker across the outside of your coop wall and part of the run.
We ran it the entire month of July last year, and our water bill was about $30 more (I don't know if that was also because we were watering the garden a lot, and filling the hot tub with cold water for us?).
In a pinch, you can always set up a sprinkler at the edge of their run/coop, and run it on low during the hottest times. Just so long as it doesn't impede their normal access to shade areas, but cools the outskirts, you're golden. A sprinkler is super cheap, too.