How about that guy on TV that replaces the bottom of a Row Boat with a screen door? I've seen that stuff at Wally Mart at the check out.
Seriously there's that stuff and the name escapes me right now but you mix it in two parts and it dries hard as metal. You can sand and I believe even drill through it when cured. I stopped an oil leak on a riding mower with it going on about 5 years now. It stands up to the heat of the engine also. If you smeared the Rivets inside and out bet it would stop the water. The name will come to me one of these days, Home Depot sells it.