ClassicCar

Based on what I'm seeing, you're looking for a pair of plates -

Here's an eBay search for you - It is an active search, so no matter when you 'click' on it (now, or a month from now), it will show you what is available at that time. I configured it for all 1930's plates, however you can easily 'narrow the scope' (1937 vs. 193*) -
EBAY Search for NY License Plates from the 30's

Best advise - Be patient, take your time. Local car events/flea markets may have what you're looking for, and you'd be surprised at some of the deals.
As an example, Fall Hershey would be a 'great' place to find something like this -

Check these out. http://www.ebay.com/sch/sis.html?_nkw=1937 NEW YORK LICENSE PLATE 3M 96 92 ORIGINAL USED&_itemId=260732663579

Of course, you'll need to find a matched pair, but it may be cheaper to buy a pair of dented ones and then pay someone to restore them, than to buy a restored set. (There are people who do that, check Google)

The price for a set is 'all over the place', however this will give you an idea as to what is a reasonable cost -

Completed EBAY Auctions Search for NY License Plates from the 1937

From this, you can see that you should be able to get a nice set of original plates for around $20-$25 (including shipping), if you are patient and keep looking/checking...

For my '46 in MD, it is a single plate (rear), with a 'year tab'. A decent plate is available for $8-$10, the year tab is $65 (Ouch!). The plates were used from 1945-1947, with tabs being used in 46 & 47, and '1946' tab were routinely thrown away, hence are somewhat scarce.

I had one (and the tab) restored - $100 + shipping, and is pretty much around the going rate for that work/service.