*Update 1/26/2017 Ok, it looks like a traditional door may not work...
What about an accordion style door? There are likely studs at both the corner and at the opposite wall on the landing that would accomodate a frame for an accordion style door. I'm thinking there would be a piece at the top to house the rollers, a piece on one side to hold the door, and a magnetic latch on the other side to keep the door closed. (We would rather not have to install it at the bottom of the stairs, for aesthetic purposes.)
In my father's house, there is an upstairs bonus room, which I will be using as a bedroom temporarily. We are trying to figure out a way to add an interior door at the first stair up from the landing in order to block out light and noise for sleeping purposes. The ceiling in the picture extends above that first step, so the door will be the height from that step to the ceiling. That height is 86.25", and the width from wall to wall is 36".
Any ideas on how to do this? What kind of door/frame to use? Some sort of folding door...?
Any help is greatly appreciated!