Stock 36V controllers can pull ~175 amps with even the most basic cart ( fleet speed EZGO ), so your battery of choice must be able to handle that and few of the 12V batteries would not trip the built in BMS in a single series string.
Something that would fit in the standard battery tray would be
6 of these, in a 2P3S configuration which should work and is lower cost than using the common 6V trojans used in golf carts