I'm playing around with a few ideas myself and what I'm coming to realize is that for a DIY type of job, at least for me, it's either a question of what I want, or what I've got. If I want a particular door design (pop up or guillotine) that might cause me to lean towards a particular drive system, or if I've got some of the mechanical parts on hand, that might cause me to choose a particular door type.
I'm not sure if you have anything in particular you are leaning towards, but I can share with you some of the things I'm trying to incorporate into my automatic door:
1) a reversible electric motor - polarity one way opens the door, reverse polarity closes the door.
2) a double pole double throw relay (DPDT) - the motor voltage will determine what the rating of this part.
3) a timing mechanism for driving the coil of the relay and ultimately the polarity of the motor.
4) limit switches for "door open" and "door closed" positions that will cut the supply voltage for the motor (the limit switches will actually be a switch + a relay since the load current will probably be high).
5) fuses
The basic design: A lamp timer with a wall wart plugged into it. The lamp timer is set to come ON during certain hours and go OFF at a certain time. The DC wall wart drives the DPDT relay to switch the polarity of the motor (ON is forward, OFF is reverse). The motor will drive itself into whichever direction until power is cut via the limit switch (or fuse in the event of limit switch failure). One design flaw I can foresee is that in the event the mechanical link between the motor and door is broken - the motor will run constantly.
I'm not yet to the point where a coop door has hit my honeydew list, but I do have some materials laying around (12v DC automotive electric window motor - power for it could be a 12v battery on a trickle charger - this would lend itself to a guillotine door) so some basic ideas are taking shape. I've got some bar napkin type sketches at the moment but that's about it. If you have any ideas or constraints you are working with just post them and we can go from there - I don't think setting up the electrics would be a big deal, and others here may have ideas for what kinds of mechanical equipment to use.