You have two separate problems - ground water runoff vs roof runoff.
Ground runoff is normally dealt with by diversion eg a ditch filled with gravel that follows the contours of the property and moves the water away from run & coop.
Your roof overhanging the run will be a continuing pita. Use eaves-trough (either plastic or metal), you will need to construct & attach a fascia board that is strong enough to hold some weight; one side only.
Ground runoff is normally dealt with by diversion eg a ditch filled with gravel that follows the contours of the property and moves the water away from run & coop.
Your roof overhanging the run will be a continuing pita. Use eaves-trough (either plastic or metal), you will need to construct & attach a fascia board that is strong enough to hold some weight; one side only.