For one, the stock.
A serial number would be required to identify the year of manufacture of your Marlin model 60.
Serial numbers were required per a 1968 firearms act. Marlin .22's produced prior to this were not required to have serial numbers stamped on the weapon and marlin decided it was not productive to do so. Although they did stamp some earlier models they discontinued the practice. My Marlin model 56 made in 1960 also has no serial number.
From my research, the Marlin mod. 80 was produced from 1934 to 1971. Pre 1964 .22s were not required to have serial numbers. Puddlejumper
Yes, marlin has now release their thumbhole stocks for models vst and vt to the public. Price is $99, but you have to call them. Their website isn't even updated enough to show the new models, let alone the stocks. The number is listed on the website however. Also, Revival gunstocks has been rumored to sell their tundra for the Marlin, but I haven't been able to confirm this since their phone lines were down when I called them. They list only Ruger 10/22 stocks on their website. This answer is assuming you are talking about the Marlin 917.
SN's were not required before 1968
Early firearms in .22 caliber were not required to have a serial number. Your Marlin 81 falls into this time frame.
Some Marlin Model 56 did not have a stamped serial number. The Firearms Control Act of 1968 required serial numbers to be stamped on weapons and since the Model 56 began production in 1955 it was not required. While Marlin did stamp some, they discontinued the practice saying it was non productive.
Serial numbers were not required until 1968.
Any firearm that was produced prior to the year 1968 was not required by law to have a serial number.The Marlin model 49 which was available to shareholders of more than 4 shares of Marlin stock was only made from 1925-1928.
Being that your Marlin model 31 was made between 1913-1916.These rifles were not required by law to have serial numbers if the manufacturer choose not to put them on the firearm.This was not a law until the year 1969.So your marlin might not have a serial number.
he Marlin Model 88 was made from 1948 to 1956. It was replaced by the Model 89. The Model 88 was one of Marlin's less expensive guns, and therefore did not get serialized. Prior to passage of the Gun Control Act of 1968, guns were not required to have serial numbers, and Marlin did not serialize many of the less expensive models. It required an extra manufacturing step that added to the cost, so it was omitted. The Model 88 would have had American black walnut used for the stock.
SN's not required before 1968