So, someone has removed them in the past and they are no longer there, right?

I know of no replacement but I would be surprised if headlamps from other similar cars ('37 Hudson, '38 Terraplane & "112", and '39 "112") wouldn't have identical rings. At least you could look for those, and measure them to see if they fit your headlight shells.

Even the rustiest headlight shells would yield up a good stainless steel trim ring. (I think they were stainless though I could be wrong.)

Once you find one, it can be coaxed off the old shell and onto yours. Just be careful prying them off, not to bend them.

As to better lighting, you shouldn't have to go to 12 volts or sealed beam lamps. A company in Australia is manufacturing a quartz halogen lamp that fits right in the original socket (with three mounting pins) AND is six volts. Brighter than original. You must of course get your reflectors re-silvered. (There is a guy in Toledo who was doing those for a reasonable fee, who did mine several years ago.)

It also helps to wire your lights to a relay, so that they are powered almost directly from the voltage regulator and not through miles of bad wiring and corroded switches. AND you could solder a separate ground wire to each of your sockets and ground the wires on the frame. In this way you can actually see the road at night, while leaving your lights with their original "look" and not changing the car's whole electrical system.

FYI
Another option is to buy a vintage sealed beam conversion kit that would take a 6v or 12v sealed beam. They were popular in the '40's to convert bucket socket Lights to Sealed Beams and occassionally show up at Swap Meets and Ebay.The Kit came with everything needed. There is a Kit for a '39 Hudson currently on E Bay but wont fit a '37. Additionally, like Jon suggested any similar headlamp ring should fit. Little British car co has 6 & 12v halogen bulbs. Google Searh and Dealer is in Mich. US.

If you are talking about the very narrow stainless steel ring around the edge of the headlight buckets, I can tell you they are very hard to find. And, many times, they are in worse condition that the headlight bucket. People who did not know how those headlights came apart would pry on them and tear the SS ring up.

I am finding that out. Have purchased several buckets only to find the rings cracked and torn up.
I have one right now I am trying to patch with some tin/ leading with out much success .

Have you tried Donald Axelrod yet? He has been selling complete headlight assemblies for all cars, for decades. He probably won't sell you just the ring, but if you're willing to buy a complete unit or set, do contact him. I believe his phone number is 781-598-0523 and his e-mail address is HDLTHQTRS@aol.com.

He is usually at Hershey, if you're going there. The fellow from Australia who makes the quartz headlight bulbs is usually there as well, though you can also buy them from Little British Car Co.