Method 1 On Route 12, go the Skiddo ranch and find the Shiny stone in the East section of the ranch accessed by riding Skiddo.
Method 2 On Route 18, there is a trainer you can fight ONCE A DAY that starts an Inverse Battle where type is cross over (Super Effective becomes Not Very Effective and vice versa). Defeat him to win one of the following prizes: Oran Berry, Siyrus Berry, Occa Berry, Passho Berry, Wacan Berry, Rindo Berry, Yache Berry, Chople Berry, Kebia Berry, Shuca Berry, Coba Berry, Payapa Berry, Tanga Berry, Charti Berry, Kasib Berry, Haban Berry, Colbur Berry, Fire Stone, Water Stone, Leaf Stone, Thunder Stone, Dusk Stone, Moon Stone, Sun Stone, Shiny Stone, Dawn Stone, Everstone, or Rare Candy.
As you'll notice, 9/28 of the prizes are evolution stones and 17/28 prizes are berries. One of those prizes is a Shiny stone.
Method 3 First, complete Lv1, Lv2, and Lv3 Normal Super Training Regiments in order to unlock the 'SECRET' Super training levels with a FULLY EV training pokemon. Complete the Lv1 of 'SECRET' Super training level to unlock Lv6 "An Opening of Lightning-Quick Attacks!".To get a Shiny stone here, complete it with a time between 2:10 and 2:20 for the best chance of getting a stone.