Should "op de kust" be accepted as well? Is there a subtle difference in the meaning? Google search for "huis op de kust" (in quotes) yields quite a bit of results.
No, the only correct answer is 'aan de kust'. I suppose 'de kust' is like a coastline, so you can be next to it but not on it. I understand that it is confusing though, because you can have a 'huis op het strand'.
Bij de kust ?