you need to find the serial number, then do a web. search for the gun maker, or others who have done the homework for you.
You can look that up here http://oldguns.net/sn_php/marlinlookup.php
Contact marlin customer service through their website.
The Wikipedia site for marlin 336 rifles includes a table showing how to use the serial number to find date of manufacture.
Try this link--- http://oldguns.net/sn_php/marlinlookup.php
There is a web site called "marlin manufacture dates", but it will only give you the year of manufacture, not an actual month and day. Seeings as you already know that it is an 1883 rifle, then you probably know as much as you are going to find out about the rifle.
While I cannot give you a specific year of Manufacture,I can say that it was made after 1906.You can find the exact year of manufacture by contacting the Cody Firearms Museum in Cody WY.There is a 60 dollar fee for a letter stating the date of manufacture and when the rifle was shipped.
For Marlin manufacture dates head to the site linked below. (see related link at the bottom)
By it's serial number.Go to proofhouse.com to find the date of manufacture.
If you provide the serial number in your question then I can give you the date of manufacture.
Starting in 1973, the year of manufacture can be determined by subtracting the first two digits of the serial number from 100: Example: SN 2512345 would have been made in 1975 [100 - 25 = 75].
You can determine the manufacturing date of a Marlin 336C by checking the serial number, which is typically located on the underside of the receiver. Marlin used different serial number prefixes over the years, and you can reference a serial number chart specific to Marlin firearms to find the corresponding year of production. Additionally, features such as the type of finish, the presence of certain markings, or the design of components may help narrow down the date of manufacture.
If you would post the serial number and model number,I can give you a date of manufacture.