You will receive a Moon Stone from Psychic Inver, the Inverse Battle dude on Route 18.
After you have defeated Inver, he will give you an item. This item is given based upon your "score" and success in the battle. You get + 1 Point for every Super Effective hit you give, and -1 Point for every Super Effective hit against you. You will get one item out of the option for the score range.
If your 'score' is between 7-9, you have a chance of receiving a Moon Stone. However, there is still a chance you will receive another stone. All the possible stones you can receive are the Dawn Stone, Dusk Stone, Fire Stone, Leaf Stone, Moon Stone, Shiny Stone, Sun Stone, Thunderstone, Water Stone and Everstone. (Yes, Everstone. xD) So it may still be very hard.
Overall, it's possible to get another Moon Stone.
Hope I helped. :)