I recently listened to a compilation album of Bobby Darin titled Mighty, Mighty Man, and I noticed something about "Down with Love" (from the album This Is Darin, which happens to be the only original Bobby Darin album I have).
Darin articulates a number of phrases in ways that draw attention to "down." The "Down" that starts the second verse is sung with a descending glissando (I think it's from C to Eb, but I found it a bit difficult to pinpoint). "Down with Cupid" in the bridge is sung to a descending phrase both times. It's even chromatic, which seems to emphasize the descent: Eb, D, Db, C. The "Down with love" that starts the third verse (a repetition of the second verse) is sung to the descending phrase Eb C Bb. Finally, the "Down" in the last "Down with love" is sung with a melisma, starting with a Bb and moving through various notes down to Eb.
For what it's worth, a few years ago, I noticed that the line "Down with songs that moan about night and day" refers to the song "Night and Day" and wrote a short post about it.