The only Pokemon that can evolve with an Oval Stone is Happiny.
If you are still playing in-game (DPPt), there is a hiker in the south-east corner of Hearthome City, ready to give you an egg. This egg contains Happiny, the only valid recipient of the Oval Stone.
Also, if you are playing post-game there is another person in Nacrene City who will give you an egg with Happiny. (BW2)
So, make sure it isn't night. (To check in BW2 you can go to Lacunosa to see if the people are not outside) and in Platinum/DP, you can check here.
When you know it's Day time, evolve your Happiny with the Oval Stone and it will be a Chansey.
Hope I helped. :)