Since you can get the stone from showing a Staryu to Bill Grandfather, that means you can only get one stone. Howver, if you are repared to cheat, you can use the Clone Cheat to get another.
Start with giving a Pokemon the stone. Go to a Pokemon Center, stand in front of the computer and save. Make sure you put the Pokémon into an empty box and save to a box which is empty. While tht text "SAVING... DON'T TURN OFF THE POWER!" appears, turn your Game Boy off. Now turn it back on, enter your saved game and you'll see that you have two Pokemon : one in your party and one in your box. Repeat those steps and get as many stones as you want.
- "Allexperts" from Google