The DT says this song is to the tune of Haste to the Wedding. The tune I know of at 'Haste to the Wedding' isn't the tune that Johnny McEvoy or I sing 'Babies By Steam' to. I'm trying to remember a name for the tune I have ... there's another song, about drink, sung to this tune...
The lyrics I sent in answer to a query at Ir-Trad-L were from memory, but I had first learned the song from a book of songs collected in Canada. The lyrics sung by Johnny McEvoy and Mick Maloney and Paddy Reilly and O J Abbot (I imagine Abbot was a Canadian source singer?) are all more or less the same, judging by the submissions from Wolfgang and others in Mudcat threads.

The County Cavan version published in Uí Ógáin, "An Rí Gan Choróin", is a bit different; I'll add it later for general interest.
I still go with my previous explanations of the basis for the song, but Ms Uí Ógáin also suggests O'Connells reputation for fathering illegitimate children story. It's said that one visit to the Ennis vicinity added 16 children to the population of Co Clare!
She says the song is difficult to date, but the reference to O'Connell's position in Dublin may be a clue. Uí Ógáin also has appenidix references to versions of this song from Tyrone,Fermanagh, Roscommon and Waterford. (admittedly, I am having difficulty understanding the reference system used -- Maybe Martin Ryan could clear up some details ... Martin, do you ever see Ríona?) I think the chapter footnotes indicate that versions of this song include numbers 212 and 240-244 in the Irish Folklore Commission collection, Cnuasacht Bhéaloideas Éireann.