That coop looks very nice!!! I am a contractor so I see what happens when people use regular lumber instead of pressure treated outside. You should be fine because your shed will be able to breath "air is moving around it. You will run into a roting problem where the pine comes in contact with the ground and is kept moist due to the ground. I would suggest you go to the paint store and buy a product called wood restorer. It is kinda like a beach that people use when they strip their decks and re-stain them. This product should be scrubed on to the wood and washed off with a hose (make sure you wear gloves on old clothing). This product will prep the would for staining and give it more of a uniform finish. I would then allow the coop to dry for a few days. Finally I would apply a stain/sealer product like you would use on the deck. Make sure that you get the sealer everywhere and you should be good. How did you cut the wood for the shed? Do you own a lumber mill?......can you send me some more pictures of the coop closer up? Thanks