First Stone
A shiny stone can be found laying on the ground in the final room of the mines on Iron Island. Iron Island can be reached via boat from Canalave city.
Second Stone
A second shiny stone can be found on Route 228. Take the narrow bridge path and follow it south past the two Pokémon Rangers. The stone will be laying at the end of the path.
Pickup
You can find Shiny Stones by keeping a Pokémon with the Pickup ability in your party. This gives the Pokémon a chance to randomly find an item after a battle. Shiny Stones become more common as the Pokémon with Pickup levels up.
Catching Pokémon with Pickup
In "Pokémon Pearl" the following Pokémon can be caught with Pickup: Meowth, Aipom, Teddiursa, Phanpy, Zigzagoon, Pachirisu and Munchlax, along with their evolved forms. Meowth can be captured in the Trophy Garden. Capturing Munchlax and Aipom requires the use of sweet honey trees: smear the honey on the tree, leave the area and return the next day for a Pokémon encounter. Pachirisu can be found on Route 205. Teddiursa requires that a "Pokémon Emerald" game be inserted in the bottom slot of a compatible Nintendo DS. Zigzagoon and Phanpy are possible Swarm Pokémon. Return to your hometown once a day and check with your rival's sister. She will alert you to what the daily Swarm is and where that Pokémon can be captured.