On Meteor Falls. No Pokemon in this game holds them. Wild Lunatones do, but you can't catch'em.
Not every wild lunatone holds them and they can only be caught in the wild in the sapphire version.
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Dawn stones are only available in Diamond and Pearl.
I think you can only find one Yes there is only one but if you had Pokemon sapphire or know someone who does than you can trade someone who has a lunatone which could have a moon stone as a held item. Of course you can give the item to any Pokemon and trade it over to emerald but a wild lunatone won't always have one and one that does is very rare. Also the emerald version doesn't have wild lunatone but solrock which are found in meteor falls and solrock carry sun stones not moon stones of which the likely hood of a wild solrock holding a sun stone is about the same as a lunatone holding a moon stone. But if you have a Pokemon that knows covet or thief you can steal one from a lunatone or solrock. Also useful move to steal held items from trainers' Pokemon.
Dawn stones aren't available in Pokemon Emerald. Use Mystery Gift.
you can trade shards for stones in hunters house. His house is southwest of mossdeep.
You can find the moon stone in Harvest Moon Magical melody in the Cave. (I don't believe that their are moon stones in the underground lake, but hey it is wroth a shot.)