As far as the coop, yeah, you might need it to be taller, so you may need a little goose house just for your geese. Mine sleep in with my chickens and ducks, but my coop is walk in height. Two feet to three feet tall is a little short for them. Especially with your run not being predator proof, you'll want to do something for them Doesn't need to be huge for two geese. Maybe make it at least four feet tall so they have some head room.