RDHD45,
Since it's a "Schoenauer", it's likely 6.5x54 MS. The same cartridge was sometimes called 6.5x53,depending on the maker, and was called 256 MS by the Brits.The rifle should be marked 1903. If it is 1908,10,or something else, then it shouldn't be 6.5. If it has a scopemount dovetailed into the reciever, the markings may be gone.
Mike
So far, I've documented 37 calibers for the Mannlicher Schoenauer. There are at least 6 distinct 6.5s, and possibly 7 distinct markings. They are: .256 Gibbs Mag, 6.5x54MS (aka .256 MS), 6.5x55, 6.5x57, 6.5x68S and .265 Win Mag.
Who knows, there may be others that haven't been documented as of yet.