After doing some research, it looks like these types of rounds are made from both tungsten carbide, and tungsten heavy metal alloys, with the heavy alloys being more common.
I have a good amount of experience machining Tungsten Heavy Alloys. In my experience, these tungsten alloys range from 90% W to 97% W with the remainder made from 8-2% Ni and 3-0.6% Fe or Cu, depending on the alloy. Technically speaking, these are not true alloys, because the nickel and iron or copper are the only materials that melt during sintering.
These are pretty easy to machine, they behave similarly to cast iron with powdery like chips. SFM 200-300 IPR .002-.008 DOC .01-.125 with a TiAlN coated, hard grade of carbide. They are very abrasive, but that shouldn't be too much of a problem if you're only making a couple of rings.