If you still have the old dead 6V item, you mây convert it into a perfectly fitting 12V type.
Carefully open the battery and take out all the lead/acid stuff. Immerse this in water and neutralize i. e. with baking soda, then depollute into the usual battery recycling system. Clean the old battery housing thoroughly. Then purchase a 4-cell LiFePO4- battery with 2000-4000 mAh capacity, either a cell block or single cells with special mounting bracket. YOu have to fit the cell array into the old battery case and make some good connections for your main power wires.
Those Lithium-Iron-Phosphate batteries are available on ebay or elsewhere. As their nominal cell voltage is 3.2 V, four of them in series form an excellent replacement for a 12V lead/acid type. No changes are necessary for R-R or alternator, but must be of course 12 Volt types.
http://www.mpoweruk.com/lithiumS.htm has basic info about Lithium-Ion batteries.
This german company
http://cs-batteries.de/Oldtimer sells LiFePO4-batteries for motorcycles. The offer only 6V types, but you should send them a request for 12V, maybe you'll be lucky ..
regards Hans