In the song "Come On Eileen," what do the lyrics "Toora Loora Toora Loo-Rye-Aye" mean?

Something along the lines of "I'll be seeing you."

An old Irish lullaby meaning "Goodbye for now. I'll be seein you"

The song is by the band 'Dexys Midnight Runners' off the album "Too-Rye-Ay" (implying the line in the question is off a little at the end). Too-rye-ay means Counting in the Kitchen(from cha cha:) The phrase "too-rye-ay" has no meaning, but is part of an Irish folk song called "Countin' In the Kitchen" originally.

https://en.wikipedia.org/wiki/Come_On_Eileen

The Irish lullaby of similar wording is "Too Ra Loo Ra Loo Ral"
https://en.wikipedia.org/wiki/Toora_Loora

Cha Cha could not come up with what that phrase means.

Twice in the first half of the song, I hear them sing 'Toora Loora Toora Loora Toora Loo-Rye-Ay' and toward the end of the song, when the beat has really slowed, I hear the background refrain as 'Eileen Too-Rye-Ay'. So it might just by an affectionate nickname lile da-da-darling and then just darling. or swee swee sweetheart. (All speculation since Cha cha gives no direct translation to either refrain. Who's the gaelic speaker around here? Lady Cat?
Interesting note is the reference to Johnnie Ray, a popular singer/songwriter of the fifties that this song singer pays tribute to as a source of warmth to his parents. His song list is impressive and one of them may also be behind the Dexy song ("I'll Make You Mine"?)

https://en.wikipedia.org/wiki/Johnnie_Ray

A video clip.

http://www.youtube.com/watch?v=oc-P8oDuS0Q