The closest thing to a bellybutton documentary that I can think of was a one hour episode of a series called "Amazing Body Parts" (I'm probably getting that name wrong). It was on one of the "educational" doc channels, either Discovery Channel, Learning Channel, or History Channel, I don't recall, this was more than a decade ago. Anyway, the episode was about "Bellies and Butts", and as the name implies, it was about the stomach and buttocks throughout history. They did mention bellybuttons for all of two minutes and then moved on. That's it.