Sometime between the mid 1940s and early 1970s.
What model????
I believe that your Sears shotgun is a Winchester model 37A shotgun that was made for Sears Roebuck And Co,.
Winchester made the Sears Model 200.
http://www.histandard.info/PDF/Sears%20Shotguns.pdf http://www.histandard.info/manuals/sears/sashotguns/index.html
Try gunpartscorp website. They have a cross reference to find the make and model of your Sears shotgun.
Its a Sears branded Mossberg 500.
The value of a Sears and Roebuck 12 gauge shotgun model number 281512651 depends on its condition. This gun in excellent condition is valued between 100.00 and 135.00 as of 2014.
The Sears Roebuck 12 gauge Model 583.606 was produced in the early 1970s. Specifically, it was manufactured between 1971 and 1973. This shotgun was made by the High Standard Manufacturing Company for Sears.
You would have to list the model number of your shotgun,to identify the maker of your sears and roebuck shotgun,in order to get the correct buttstock.
Sears Slug Model 446.511761 is a Mossberg 500. All parts interchange.
Winchester 1200