Blue Book says Winchester 57 was made 1926 to 1936.
I think all those Winchester side-button .22 magazines are the same. Numrich has aftermarket replacements.
http://www.e-gunparts.com/product.as...KU=294390A&MC=
Some discussions on them in Rimfire Central, like:
http://www.rimfirecentral.com/forums...=winchester+57