I have no idea whether or not this is the item included in "Riverdance" but for what it's worth -- this is the text of a Scottish Gaelic port a beul ("mouth-tune") recorded by Mrs Archie MacDonald of South Uist for the School of Scottish Studies, University of Edinburgh. It's published on a mono LP released by Tangent Records (TNGM 110) in the 1970's. The liner notes include the following:

"The words of puirt-a-beul are composed to dance tunes, normally strathspeys, reels and jigs, and hence are almost always short, the standard form being of two verses. Often enough the words may have served as no more than mnemonics for the tunes, but there is evidence that puirt-a-beul were sometimes actually danced to when no instrumentalist was available. The words are generally of no great significance, although they are often very deftly put together....[P]uirt-a-beul are for the most part anonymous."

Fosgail an dorus dh'an tailleir fhidhleir/ Fosgail an dorus dh'an fhidhleir thailleir/ Fosgail an dorus dh'an tailleir fhidhleir/ Cliamhain a' righ fidhleir tailleir.

'S dileas mise dha 's cairdeach mi dha/ 'S dileas mise dh'an fhidhleir thailleir/ 'S dileas mise dha 's cairdeach mi dha/ Cliamhain a' righ fidhleir tailleir.

Bainne nan gobhar dh'an tailleir fhidhleir/ Bainne nan gobhar dh'an fhidhleir thailleir/ Bainne na gobhar dh'an tailleir fhidhleir /Cliamhain a' righ fidhleir tailleir.

TRANSLATION

Open the door for the fiddling tailor /Open the door for the tailoring fiddler/ Open the door for the fiddling tailor / The King's son-in-law is the tailoring fiddler.

Faithful am I to him, kinsman am I to him/ Faithful am I to the tailoring fiddler/ Faithful am I to him, kinsman am I to him/ The King's son-in-law is the tailoring fiddler.

Goats' milk for the fiddling tailor/ Goats' milk for the tailoring fiddler/ Goats' milk for the fiddling tailor/ The King's son-in-law is the tailoring fiddler.