Didn't know if you meant plex doors or rail doors so i made both...
Plex:
Flipflop is turned on and connected to door blocks (activated plex doors are closed).
The button will turn off the flipflop (which opens the door) AND start the delay timer.
The last delay block turns the flipflop back on, closing the door.
Rail:
When a button or an activation module is touching a rail it turns on when a docker passes over that rail.
A button makes the rail go up.
When the rail docker reaches the top it starts the delay timer.
Last delay block makes the rail go down again.
Hope it helps.