Using a good exterior paint would last the longest, you could buy the smaller quart sized containers of just primary colors and mix small batches for each color for your mural. If you don't like mixing your own paint colors you could try acrylics and seal it. Here in the south the sun tends to fade paints much more quickly though and I've never found anything that has the same staying power as Duramax, which is an exterior latex paint. As long as you allow most paints to cure and offgas sufficiently, it should be safe for your chickens. I painted my first coop inside and out with Duramax with no issues. I hope you'll share pictures when you're done!