Like many old songs (if it is one), changes probably took place as it was handed down. I have not found sheet music on the internet in Library of Congress or other collection under Irene or Good night, although there are several songs by Gussie L. Davis, who seems to have done mostly minstrel-type songs.
As things stand, it could be credited to Lead Belly's uncle Terrell, the source according to Lead Belly in an article in Time Magazine.

The article quotes two of the original verses, which are not sung on the usual recordings that I have heard although he sang the last one at a concert at the University of Texas about a year before he died. With his leg in bad shape, he was escorted on and off stage by his wife. An unforgetable evening. At the time, there was only one black student on the campus; a law student named Sweat, who was taught in a separate class, forced on the University by the courts. At the time, a popular deoderant named Mum was sold. A sign on the campus announced: "Mum's the word for Sweat."

I ask your mother for you,
She told me you was too young;
I wish to de Lawd that I never seen your face,
I'm sorry you ever was-a born.

I love Irene, God knows I do,
Love her till the sea runs dry.
An' ef Irene turns her back on me,
I'm gonna take morphine an' die.

Copyright 1950, Spencer Music Company

The website: http://ourworld.compuserve.com/homepages/JimCapaldi/timeiren.htm : Good Night, Irene