Pretty much any paint you can buy these days is nontoxic when dry. Pretty much all of them have fumes that you're better off not inhaling when they're wet.
So, really ANYthing will do, just make sure it is fully dry and well aired out (takes hours to weeks, depending on type of paint and coop ventilation and your climate/weather) before chickens go in, and you're good to go.
If you use stain or polyurethane you will have to reapply it sooner than you'd have had to repaint, BUT you can just wash and lightly sand the surface and do it, won't have to scrape up peely stuff as you have to do with paint.
If you use paint, it will last a bit longer between reapplications but involves more work (scraping). If you are going to paint, it is very important to prime well first, and then to apply thin rather than thick coats of paint.
Good luck, have fun,
Pat