Model I S2's had the chrome dial faces, and Model II S2's had the black dials. Model II (15,000 produced) serial numbers range from 6135001 to 6198380, with production ending in March 1958. That's about as specific as I can get on the body, so yours is towards the later production.
I don't have a lens serial listing, but some things to look for are the markings on the name ring. Does it say "Tokyo", or "MIOJ" (Made In Occupied Japan), or "Japan"? The first two are from the earlier production runs, prior to 1953. If it says "Nippon Kogaku Japan", then it was made starting in '53, and was on the sales list until '62.
Info from
The Complete Nikon System by Peter Braczko
PF
ps: Hey, I just found out where I stashed my
Nikon Rangefinder by Robert Rotoloni. He shows that production began on the post-occupation 50/1.4 at 322000, and ended with 417862, so yours is kind of middle of the pack. He states that the screw mount lenses were included in this production run, and could account for about one third of the total (90,000 to 100,000 in all) but were likely in the early production as they were being supplied to Nicca and others using the Leica screw mount. One thing though, at number 374000, they switched to an aluminum barrel painted black (with chrome filter ring). So the black barrel lenses are lighter. Again, he didn't give a year this change was made.
You can also do some reading up about your S2 on the Head bartenders excellent site at
https://www.cameraquest.com/nfs2al50.htm