I posted a small tip on making rings with the Punch & Die set earlier. I now use my lathe.
I use stock styrene rod from Plastruct. I drill in the rod with the correct inner diameter and use the lathe to remove enough material for the correct outer diameter (example in the image shows this in reverse). Instead of using a parting tool, I reinsert the drill and use a knife to cut the ring from the rod; the drill with catch the ring. You can make a series of rings quite quickly and collect them on the drill. Using the knife can result in some variation of the ring thickness, but the number of rejects is a lot smaller than with the punch & die set and I can now make rings of all sizes. You do need to be careful using the knife while the lathe is rotating; this is why I position the knife as in the image—cutting with and not against the direction of rotation—so that the tip of the knife can’t be hit by the jaws of the chuck and catapult into my eye.