A DRINK IN THE MORN is performed by Packie Dolan and the Melody Boys on the various-artists compilation "Ballinasloe Fair: Early Irish Music in America (1920-1930)," Traditional Crossroads CD #4284, 1998.

(I don't know where Mortimer Rabbit comes in.)

CD Universe has a sound sample:

...draw my cruiscín lán away,
Then who'll drown the shamrock on St. Patrick's Day?
In winter or summer, in June or July,
I'll drink poitín till the day I die....

[The tune is a pleasant waltz.]