The Rufus comments reminds me of another song....

"T*ts" by Sparks. 
Which is about a new family. But, sadly it's also is one that would 
fall under the "NOT suited" for what your looking for (celebrating the 
joy of a new baby)...especially not suited for the new papa. Given the 
sad sack, drunken, neglected new daddy in the song's story.

Steve D