[Accessible Japan]

The place I found had a 3hr route for 18,600 yen, a 4hr route for 24,700 yen, and 4.5hr route (including Shirakawa-go) for 27,800 yen.

Here is the site: http://www.kaigo-taxi-hiyoko.com/kannkoumoderuko-su.html

As for renting, they do exist, but I think @wilgo checked and one place required a Japanese license…