Without any further info on your specific firearm, the only dates that I can give are from 1937 to 1987. Ithaca made several different variations of the Model 37, some of which went out of production before others. Production did start in 1937, and the last variations of the Model 37 were replaced by (or renamed to) the Model 87 in 1987.
Model 37 standard, made in 1941
about 23$
Call Ithaca at 1 877 648 4222 and they will tell you.
Made in 1939
Made in 1963
1963
1972
1973 - Ithaca Model 37 Featherlight
Your model 37 was mfg. in 1972.
your Ithaca model 37 is made in 1966 look on WWW.SURPLUSRIFLEFORUM.COM look for in the "search engine" on that web site type in ITHACA 37 DOM there you'll find the Serial Number chart
You Model 37 was mfg in 1954.
The serial number indicates your Model 37 was manufactured in late 1969.