Actually, a friend of mine just suggested an interesting idea for an automatic coop door involving two pulleys, a coffee can with a small hole in the bottom, a five-gallon bucket of water, and a small fountain pump on a lamp timer. Here's his description:
"Put a vertical sliding door on the coop. This has a rope on the top to a pulley, over to another pulley, attached to a coffee can with a pinhole in the bottom. Under the coffe can is a five-gallon bucket of water. Put a fountain pump in the bottom of the bucket, that when turned on by a lamp timer will pump water up and into the coffe can. In the morning, timer turns it on. Pump pumps water into the coffee can faster than the pinhole in the bottom will let it out. Once can reaches a point, it gets heaver than the door on the other end of the pulley.
At night, pump shuts off. Coffe can drains, gets lighter than the door and the door lowers itself shut."