I'm not sure that is really from an actual song. Rather than that, it is supposed to be the classic stereotypical funky-style "porn music" to imply that the stork and the woman are indeed about to make that baby right now, as also implied by the red light the stork installs and his whole behaviour.
This kind of cliché "porn music" is a common trope often used in a comedic way to signal that something sexual is going on or about to happen, like in this scene. A variation of this trope is when characters utter the words "bow chicka wow wow" in a melodic way in order to immitate this funky music and in turn imply something sexual in a funny or satirical way.
I'm not sure how extensive this Family Guy wiki page is and I have only checked it roughly, but it doesn't seem to list the song explicitly as reference or music used in the episode/movie.