I had an inner tube installed on a front tire by my local motorcycle shop because the tire on had 500 miles on it. Filled it with nitrogen to keep the moisture out and I would top it off only with compressed nitogen. 10k miles with no issues with it.
They wont patch motorcycle tires....
Bridgestone had made the front tube..
but doing a quick search.. I found a Continental F/G 16 for the rear.
http://www.conti-online.com/www/motorcycle_de_en/themes/tubes/motorrad_schlaueche_en.htmlfor the labor of doing a rear tire, just get a new tire.