I have used die punches for cutting various felt and leather punchings.
They come in numerous sizes, are approximately one inch tall and not
too expensive.  There may be a minimum order however.  The company
I have bought from is http://wagnerdiesupply.com/  Also, I purchased
some die punches on eBay a while back.

I find the "feed through" punches to work best.  If larger diameters
are needed they can be made by bending flat die stock to the desired
diameter.  It also is about one inch tall and comes with one edge
razor sharp and the opposite edge flat.  Either the ready made punches
or the flat stock should have a "backing plate" so the blow from a
hammer will be distributed evenly.

It is also very easy to make punches for leather or felt washers by
using two punches of the desired diameters and wrapping masking or
other tape around the smaller punch until the wrapping fits the inside
of the larger punch.  Only one or two punchings at a time can be made
with the washer punch arrangement.

George Cooper