Just looked it up - apparently the SOFA was renegotiated a few years ago (I remember hearing something about that).
The following information was taken from this page:
http://www.irwin.army.mil/HQGarrison/Staff/Logistics/CountryInstructions-Germany.htm
(similar information at a USAREUR web site)
Privately Owned Firearms (POFs)
To avoid the possibility of German criminal prosecution for unauthorized possession of weapons or the possibility of punishment under the Uniform Code of Military Justice, privately owned firearms will not be shipped, handcarried, or transported in luggage to Germany until further notice. The ownership and possession of privately owned firearms is prohibited by German law unless the owner has a German Weapons Possession Card(Waffenbesitzkarte). Headquarters, USAREUR and German Federal Ministry of the Interior are developing procedures to enable military and civilian personnel assigned to Germany and their dependents to obtain these cards through the USAREUR Central Registry. This instruction will be modified or rescinded when the weapons permit procedures are finalized and implemented. (CH)