Hi, I just wanted to add that in my backyard, we diverted water with 8 inch tall mini-berms. Because of the tree roots, digging a trench would be difficult, hurt the trees, and likely fill up with leaves anyway. So I built up a mini-wall instead. It's a v shape, with the point of the V uphill, and the thirty foot legs protecting the house. I used two garden timbers, and connected them with aluminum spikes - they look like foot long nails, that were rust-proof and long enough to go into the dirt a little. I pre-drilled the holes, a little big, so the whole thing pulls apart if you want, but it seems to be stable out there even with the dogs. I mounded soil against it on the downhill side, and I wanted to put some rock on the uphill, but never did. I got some leatherleaf ferns to grow in the new soil. It's made a huge difference for heavy rains and snow-melts.
Another thing to try depending on your topology is a rain garden, where you dig a dip and plant water loving plants, making a bog to catch the water and let it slowly absorb into the ground.
Remember to check drainage off your driveway and house, too, and maybe the septic drainfield. That can pre-saturate the soil by the coop, which makes everything worse.
My suggestion would be a layer of gravel and sand. When my run started to get muddy in Fall I spread some grit around as a desparate let's-see-if-it-works thing. Amazing how quickly it worked! Since sand is good for drainage and gravel is heavier it won't wash away. You could always put hay/ straw on top, that's what I did. Every now and then add more gravel and sand as it gets pushed into the ground. Chickens can peck at it for grit and the run won't be muddy. Good luck
