There may be lots of smaller batteries that will fit the original battery tray, limit about 6-1/2 inches square at the base (7 inches max length if you leave out the rubber pads). Common problem with the smaller batteries is insufficient storage capacity. The original twin 6-volt batteries had 58-AH storage capacity. That was handy for over night running if the generator didn't quite keep up with total power consumption. You could also leave the headlights on for a while when parked (up to 2 hours when new) and still be able to start the engine. If you install an alternator to keep the battery fully charged at all times, then you can get away with a slightly smaller battery, but do pay attention to the cold cranking amperage capability).

Here is one of the smaller candidates built with AGM materials, notorious for HUGE cranking capacity numbers. However, they typically have smaller storage capacity because the batteries are built physically smaller. The Braille B3121 is an appropriate model number, having 31-AH reserve capacity and weighing 21-Pounds. Dimensions for this one are 6.6” x 5.2” x 6.8", so you might even be able to lay this one on its side in the original battery tray (without the rubber pads). With only 31-AH storage capacity you might worry about leaving the lights on for an hour or more. I don't know what deep discharge does to an AGM battery, but I suspect not good. It is also three to four times the price of a standard lead acid battery, but definitely maintenance free. See the manufacturer's web site here: www.braillebattery.com