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I don't have a specific recommendation, but a lot of folks use lawn tractor batteries. I would think some of them would have round posts (I know my Dad's 1969ish Cub Cadet had round posts). Or- if that doesn't work, get some flat connector wires? The ground just goes to a transmission bolt and the hot goes to the starter.
Look for a U1 or U1R ( posts reversed).
I did start to check into a tractor battery but from what I was reading most of those were deep cycle and a deep cycle is designed as a "starter" battery, so the cells are designed to take a charge from a battery charger then you can run it till it dies, then charge it again. Whereas a car or motorcycle has a constant charge running through it. Something about plate thickness affecting a constant charge, so they're best for vehicles without a charging system. I'll give them another look though. Thanks for your input, much appreciated.
The original battery had small "automotive" type posts, no battery with those is currently available. If it has battery terminals for that, then it needs new cables anyway, since they are 50+ years old. It's possible that the owner fitted a first generation Mazda Miata battery, which has "normal" sized automotive posts. This is one of my favorite batteries as it fits the battery frame very well, only requiring that two plastic tabs be trimmed away. https://www.batterymart.com/p-12v-mazda-miata-battery.html
Farm & Fleet has lawn tractor batteries with round posts. These are not "Farm Tractor batteries" they are lawn mower batteries. And as mentioned a U1 or U1R type.