How about this?
You put in a request for a movie, and when the theater gets enough local requests, they schedule the movie.

There used to be a theater in town that would show a double feature of old movies for a couple of nights, then switch to another double bill. It was great - you could see 6 different movies in a week, all on the same screen.

I guess they didn't make any money, though, since they went out of business.

But maybe with new tech, they could show digitized movies, which they'd get electronically from the distributor once they got enough commitments from patrons.