I don't know why you would want to calk the inside of the coop... But, I would use an outdoor rated, paintable caulk.
Acrylic is easier to work with and cleans up better than silcone. Silcone will last longer and is more flexable over its lifetime than acrylic, but is harder to apply, takes longer to dry and it smells. Acrylic is less expensive than silcone. I would probably go with an acrylic, and reapply as needed after a few years.
http://www.doityourself.com/stry/acrylic-caulk-vs-silicone-caulk