I need more then one trying to complete the pokedex
Recently asked.
Walking around with a Pokemon with Pickup. (Four percent chance at levels 41-60, 10% chance at levels 61-100.) Secret Super Training (Drag Down Hydreigon)
http://pokemondb.net/pokebase/262573/where-find-moonstone-pokemon-omega-ruby-and-alpha-sapphire
Both of these would map over to Y. Unsure if Inverse Battles would as well, I only ever did it once so I don't remember his prize structure in X/Y. Pick-up is very effective.
You can thief/covet moonstones off of Lunatone and Clefairy, and at a certain level have a chance of Pick-up handing you one, if Super training isn't coughing one up.