Right! The only place I can find this verse in print is in Sam Henry's SOngs of the People, as published by Huntington etc. some years back. They quote Henry as follows:

' The exigencies of rhyme required the humoroius substitution of "the great titter-a-tally o", the reference being in all prob to Daer, of Shronhill, near Tary, the richest man in Ireland abouit 1800, or it may be a corruiption of "reat tetrarch Ali O!" as the old song makers were very fond of learned allusions."

The only earlier wsource of the song of which I know is in the first issue of the Journal of Irish Folksong society (1904). Two versions are given, one from the same source as Henry's. Neither use the word.

Regards