You can find them in: Optional mission, Random Treasure Chests, Random Kecleon Shops in Mystic Forest & Joy Tower.
Source: http://www.serebii.net/dungeonsky/items.shtml Just hit Ctrl+F and type Moon Stone to find it specifically.
The Moon Stone can be found on Optional Missions, in Random Treasure Chests, Joy Tower and the Mystic Forest Kecleon shops (at random).
Hope I helped. :)