@ late 1975 or early 1976.
Date of Mfg. is 1947
1951
1955
1950
The serial number indicates Ithaca manufactured your Model 37 in 1956.
1947
Ithaca started manufacturing the Mod 37 in 1937 with serial number 1. It has a serial number somewhere - look on the bottom of the receiver. Go here to determine the date of manufacture: http://www.diamondgunsmithing.com/
Who made it? What caliber/gauge?
All production models of the Mod 36 and Mod 37 manufactured in 1998 or later are rated for +P ammunition. Prior to that date, no guarantees.
Ruger has extensive serial number data on their website.
http://www.diamondgunsmithing.com/page5/page23/index.html
Call S&W and they will tell you when it left the factory.