If you are forced to build the coop downhill of the run, I would (strongly) suggest three things:
- make it a raised coop, not dirt-floored, and don't just use blocks, use posts WELL SET DEEPLY into the ground (there may be erosion/settling around them...)
- contour yourself a swale uphill of the coop, leading around and away from the coop, to intercept the water running down from the run. You want to leave a few flat feet between the coop and the start of the swale, and make your swale gently-sloped not a steep narrow trench. It will probably take at least a few rains/floods for you to get it 'tuned' to where it collects and diverts water properly; and then if the chickens take it to bare dirt, it may need periodic tuneups as the years pass.
- do your utmost to keep as much vegetation in the run as possible, meaning have as few chickens in as large a run as you can possibly bring yourself to make. Bare earth will erode and cause all sortsa problems, in proportion to how steep the slope is.
Good luck, have fun,
Pat