From what I could find:
Wiki:
A converted 230 G Geländewagen was built for John Paul II's visit to Germany in 1980.[1] One of the current models is actually based on an M-Class sports-utility vehicle built in the United States. The ML430-based popemobile was presented to John Paul II in June 2002.[2]
In addition to his M and S-Class, Mercedes has put together another ride for the Pope. This "Fair Weather Popemobile" is a new G 500. (Current "convertible")
( In 2002, Pope John Paul II requested that the media stop referring to the car as the Popemobile, saying that the term is "undignified".)
No info on the dressing, though.