You want to mount the batteries as close as possible to the supercharger to minimise the weight of the wires connecting them and the losses in them.
Do you have an idea of what the duty cycle of the supercharger is going to be? The hybrid battery from something like a Fiesta would seem appropriate based on a few guesses.
HYBRID BATTERY FORD FIESTA 2020 2021 48V 8AH LX7A-10B759-AD 2495700 BOSCH | eBay
Also, how do you intend charging the battery?
Do you have an idea of what the duty cycle of the supercharger is going to be? The hybrid battery from something like a Fiesta would seem appropriate based on a few guesses.
HYBRID BATTERY FORD FIESTA 2020 2021 48V 8AH LX7A-10B759-AD 2495700 BOSCH | eBay
Also, how do you intend charging the battery?