When I just want to clean up the hole and ease the edge, I stick the corner of a sanding sponge into the hole and give it a few twists.
When I want an actual roundover, I chuck up a roundover bit with the desired radius in the router table. This presumes the hole diameter is large enough to accommodate the guide bearing on the bit, obviously.
you don't say what size hole and what radius roundover you want. And how close to really round you want it.
For large holes (e.g. 3/4" and larger) I'd use a roundover router bearing bit and make a few quick light passes.
For holes about 1/2" and smaller, I'd use a countersink bit to break the corners, at smaller sizes an ~45° countersink is as good as a roundover. For more rounded, you could then follow with some sandpaper by hand or even a dremel tool and some of those cone-shaped abrasive bits.
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