The Irish Descendants (note spelling) recorded THE DUBLIN REEL; it is on their albums "Rollin' Home" (1998), "We Are the Irish Descendants" (2004), and "So Far So Good: The Best of the Irish Descendants".

It has the refrain:

They were dancin' all night long,
Dancin' till the break of dawn.
They were dancin' all night long,
Dancin' till the break of dawn.

...but I was unable to find complete lyrics.

You can hear a sound sample at The Irish Descendants' web site, but it contains no more lyrics that what I have posted.

This song has been requested before, in the thread Lyr/Chords Req: Dublin Reel (Irish Descendants), but no one came up with the lyrics then, either.