If the car is a 1951 it would've originally had an Autolite electrical system. It's probably a good idea to verify that as some cars have had their engines replaced over time and if it were replaced with an engine from a 1952-54 Henry J, it would have Delco-Remy electrical components. If it is the original Autolite, the regulator number is Autolite VRP-6001A. It can be replaced with a Sorenson AL507, a Neihoff AL156E, Filko VRA-345 HD or a few others. I believe Napa still sells one that works. If it's 6 volts, 35 amps and wired for Autolite (terminals from left to right are "ARM", "FLD" and "BAT") it should work.
Check ebay, they often show up there.
PS - The standard (four cylinder) and Deluxe (six cylinder) HJ both used the same one.