Do you have the height available to put in a pair of 6V golf cart batteries? That would likely be the best bang for your buck provided it would work. There are also 12V GC12 batteries available that are a little different form factor; you might be able to fit one (but not two) in where a pair of 6V GC2 batteries would not fit. The 6V ones are far more common and somewhat less expensive per Ah.
Actual deep cycle 12V batteries in standard car battery size are rather hard to find and are consequently rather expensive.