Ray, if you would do as John(JT) has suggested, you would end up with no more then a dimple in the center of the disc. Al you would need to do, is have the piece of wood your jig is made out of, to be thick enough for the nail to be held firmly into place. Now what I'm thinking of is for scroll saw use only, but the jig could be made very much like the ones used on a drill press. I hope that this explanation will work, and that it's not to long to read.
But if you were to take the piece of wood, you plan to use as a base. And you cut a kerf into it, so that it could be moved farther from or closer to the blade. Then add stoppers to the underside, so that it can't move any from side to side. Then with it still in place, mark a line that runs 90* from the front of the blade to the right or left. I prefer the right hand side, but you choose. Now, remove the base, which should be no less then 5/8th" plywood or mdf I prefer 3/4"plywood. Do not use OSB or Particle board, they are not strong enough. These holes have to be very close to the size of the nail, so that there is no movement in any direction. But, they also can't be so tight, that they cannot be easily removed. I'd suggest a 2 1/2" nail be used as your pin, you cut it off so that no more then 3/32" is up through the drilled hole. You will have to sharpen the tip of the cut-off nail to a point. And you should also drill the underside of the base, with a bit just large enough for the top of the nail to sit into. Doing so, will help hold the nail in place better. This should work, but you will only be able to cut circles that are within 3/8" to a 1/2" larger or smaller then the other. It would depend on how far apart you drilled the holes. Now, if you were good at using a router, there's an adjustable one that you could make. It would be almost the same, as the ones used on a bandsaw and adjustable to any size as well. There's numerous ways of making one of these, and they're not that hard to make. You could make an adjustable one, just using a tablesaw. This is something that I never imagined would be requested for scroll saw use, but to each their own. But, I suppose one could come in handy, if you had a lot of circles to cut. I make no guarantees that this will work, I just came up with this idea after reading the posting.
Len