In Pokémon Emerald, a Dawn Stone can be obtained in the following locations:
Route 111 (Desert): Search for a hidden item buried in the sand.
Lilycove Department Store: After obtaining the Devon Scope, visit the 5th floor and purchase a Dawn Stone for 3,000 coins.
This evolution item is used to evolve certain Pokémon, such as male Kirlia into Gallade or female Snorunt into Froslass.