this is copied from a site, the web address is pasted below.
The serial number depending on the model of rifle, will be located either on the upper or lower stock tang, or side of the receiver.
also if you find serial # you may find more info here.
From 1962 thru 1968 Marlins rimfire rifles (other than the 39 series lever actions) used a two letter date code that was stamped on the barrel. This date code is different than the one already listed, as Marlin rimfire rifles (other than the model 39 series) did not have a serial numbers until required to by Law after 1968. The first letter of the date code represented the month of manufacture while the second letter indicated the year. This date code was usually stamped on the left side of the barrel just in front of the receiver.