Well, the Barnard College radio station (WBAR) lists a song in its playlist a called IT'S SOMEBODY'S BIRTHDAY TODAY. The artist is Desparate Bicycles, and the album is "Remorse Code." Somehow I doubt that's the one you're looking for.

Also, there's a children's song called SOMEBODY'S BIRTHDAY TODAY, written by Frances Dillon and Christopher Hedge, and recorded by Frances Dillon (known as "Francie") on an album called "Toy Box." CD Baby has a sound sample, but that doesn't sound like your song, either.