I'm 100% sure on this, get the Shiny Stone, trade for the Carbo Cookie, give the Carbo Cookie to the kid on the bucket, then you either get a chance on the Midas River and keeping your coins, or get a Frog Coin. Keep repeating that, and he'll keep getting more.
By the way, he tells ME to come back later after I buy the FIRST set.
Mario, Mario, Mario! What happened to Mr. Andretti?