don't use diff oil it has additives for hypoid gears (gears that aren't centred axis to axis - like diff gears - where the teeth slide across one another - it's not the best for anything else. Additionally, the viscosity is rated differently, at 100C it will thin out to something like 5w30 motor oil (or roughly dexron auto trans fluid).

About the best gearbox oil I know of is Shell Donax TD in 5w-30. It is used in industrial and agricultural machine gearboxes, and a friend via the internet who also operates fleets uses it in (in his words) everything that has a manual gearbox. In essence this is the sort of 'treatment' the oil would be subjected to in the supercharger.

If I couldn't use Donax (it's not available in smaller containers, but at least you could use it in the gearbox in the car as well) I'd suggest auto trans fluid - probably dexron. Dexron itself is up to what - 5 or 6, and although it's backward compatible, it is thinner than dexron 2d was. I think Transmax M (or something like that) is one of the few still available dexron 2 spec auto trans fluids, but might be getting the name confused.