EdS has got the right idea! In fact wooden boat builders would do this in reverse, and go under the leaky boat and let the sawdust go up. So go get some cedar sawdust.
Then you can think about whether or not you need to use some epoxy resin on the bottom of the tub. You can get clear resin, and mix some of the sawdust into it, or you can get resin, and laminate cedar veneer into the bottom of the tub.
Some really hotshot boats (custom built high end yachts) are built with this technique -- laminating wood veneer with resin -- I think it's called "cold molding" or something like that.
I think a stop leak product for an auto radiator would make a big smelly mess, and might wreck the whole thing. I would strongly suggest you discard that idea. Good Luck!