You get a shiny Gyarados in the Lake of Rage in GSC and HGSS.
If you register every non event Pokemon in B2W2 in the Unova pokedex, you get a permit to the nature preserve, and in there, you can find a shiny Haxorus.
After defeating Benga in B2W2 in the Black Tower or White Treehallow, he will give you a shiny Dratini or Gible.
In Legends of Arceus, you can get a request called A Peculiar Ponyta, which you get after beating Kleavor. It is found in the Obsidian Fieldlands.
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