Count the lands a grooves at the muzzle, the Ballard barrels should have only 7 grooves for the 22, the Micro-Groove barrel will have 16 if I remember right.
The link below probably has more information on the Marlin barrels than you want, but it's worth reading.
Marlin Microgroove Barrels
The letter date code on your rifle is most likely a D (1947) if you're sure it's Ballard rifling, as there is no B and the R is 1957-58. The Micro groove was started in 1953 on the rimfire barrels.