colin replied the topic: Using a router to make small circle cuts
I also didn't ask you what you are going to be cutting, that may have some bearing too. I think for cutting holes, I would use a hole saw rather than a router. Hole saws come in almost every conceivable size and if you have a decent sizes drill to drive a bigger saw, this might be the quickest and safest.
You might even be able to cut the ring with a holes saw, but if not, I think I would try to find something on hand that you could fasten down and use as a guide for the router to run on the inside of, but his may be easier said than done.
Next would be to make a temporary circle jig for your router from some thin plywood. There are many examples online of what these look like, in your case it would just be a simple one-time jig.