Need Help...1987 Cooper Battery Replaced with a '96 Corolla battery possible?

I have a question for a friends Mini Cooper.
It is a 1987 model.
The battery isnt that great...
does anyone know whether it is possible to replace the battery with a '96 Corolla's battery?
The corolla is all we have at hand at the moment, if there are any other possible suggestions, we are open to any suggestions.

plz and thnks