The cheap way? take some sandpaper to the inner ring to rough it up and increase surface area. Take a rag soaked in water, preferably without a neutral PH and rub it around the inner hole for about 5 minutes, resoaking the rag every minute or so. This will help dissolve the feldspars in the granite. Immediately after while still wet, stick it in the freezer for an hour. Pull it out and let it come to room temp. The water will have soaked into the areas of dissolved feldspars, frozen, expanded, and chipped out undissolved material. Repeat this process about 50 to 100 thousand times, and you will probably get close to the 2" diameter.

Or get a stone router bit like these and work the inner circle until its the desired diameter.