You don't mention what sort of gun we are talking about but if it is one of the little CVAs with barrels only 3/4" across the flats, that could be rebored no larger than .410 and a black powder .410 is not much of a shotgun, especially with a barrel length of less than 30" and no choke.
Reboring a barrel is not inexpensive so I would think that a costly way to get a not very useful shotgun. I'd suggest you talk it over with a barrel maker like Ed Rayl who could do the work, do it very well and tell you what to expect both as to cost and as to performance. If you give up the idea after looking into it you will at least have learned something for the cost of a phone call. I have a 32 gauge, .53 caliber, with just a bit of choke which handles 3/4 ounce of shot and patterns very nicely, a good small game gun out to 25 or maybe 30 yards.