Are there any Pokemon that evolve with the shiny stone in black an white?

No, there are no Pokémon that evolve with the Shiny Stone in Black and White.

The Shiny Stone was introduced in Generation IV (Diamond, Pearl, and Platinum) and it is used to evolve:

* Roselia into Roserade

* Minccino into Cinccino

These evolutions are still possible in Black and White, but the Shiny Stone is not obtainable in those games.