When a tubeless tire is mounted on a rivited rim, air leaks around the rivit holes, right? You could take the tire off, weld a bead around each rivet, carefully, grind smooth, paint(heavily over the welds) and mount tubeless tire. Sometimes the valve stem hole for a tube type rim wont accept a tubeless valve stem and the only option then,AFIK, is to weld the hole shut and drill a new nole for the tubeless valve stem.
Another possible option is to use the spray undercoating on the inside of the rim. If air still pushes out around the rivets, try duct tape around the inside of the rim. A tube is easier but more expensive.