The correct rivets were oval head tubular wrought iron with black enameled heads. 9/64 (shank dia) x 3/16 (length) 15/64" head diameter.
The service replacements were Oval head, tubular, steel, Nickel plated (bright), same dimensions as above.
You can still buy this type rivet. There are several tools made to set them by hand. The brake lining rivet sets work quite well. Or in a pinch a pin punch followed by a larger flat tipped punch will do a nice job. Just google tubular rivet and you'll get tons of sources.
54 M37, 66 M101, 45MB, 51 M38, 60 CJ5, 46 T3-C
Disclaimer: Any data posted is for general info only and may not be M37 specific or meet with the approval of some esteemed gurus.