Though a door may limit the way you install your blinds, it's not impossible. You can't use an outside mount since it will restrict the door's movement, and you can't install an inside mount on the door since most doors do not have enough space, but you can install an outside mount-type style on the door itself.
Install the Brackets
Measure 2 inches from the outside of either side of the window. Mark with a pencil. Find the center of the window. Measure 2 inches above the window in the center. Mark that spot.
Use a level to check the markings.
Drill holes in the three places above the window.
Place the brackets over the holes and put the screws in the bracket holes.
Install the Blinds
Hold the headrail of the blinds so that the front is facing you.
Slide the headrail into the brackets.
Snap the headrail into place. You'll have to apply pressure and you'll hear a click when they're in properly.