Unfortunately, it is larger batteries you need, not smaller. The moto batteries may have enough energy to make a few cups, but the rate that the machine tries to take current from the battery is far too high and as such the internal resistance of the batteries will cause them to heat and explode!
Mabye with 6x12v, giving 72v total, the current requirement would be acceptable for them? Again, you'll need a custom invertor though (most likely a custom made transformer?) and i'm almost certain it is against school policy