Hi MPP,You obviously mean the part of Gay Wellington (she's there when the curtain rises on the second act, has lines at the beginning, middle, and end of the act, and is passed out on the couch for most of the act) but I don't see her singing anything in the script. There must be more than one version of the script. If you give us all the lyrics that your script has, we can probably come up with the rest of the song. Or, sing it to the melody of the limerick song. It's certainly a plausible thing for a drunk to sing.
Maybe someone else can provide a link to the melody of the limerick song.
Good luck with the audition!
Jacob