Rheinbayern was the region immediately to the NW of Baden. It was ruled (owned) by the Kingdom of Bavaria, but was not contiguous. It goes under a number of other names including: Bavarian Rheinland-Pfalz, Rheinpfalz, Pfalz, Palatine.

Many used this area as a staging area to leave old Germany (apparently because of its religious tolerance).
http://www.genealogienetz.de/reg/RHE-PFA/rhein-p.html

Bavaria (called Bayern in Europe) is a large state east of Württemberg.  Rheinbayern combines the Rhine river with Bayern as a place.
Not exact but not too far off.