I don't think this is complete but it is a pretty good start.
12th Of July
All I Remember
Change In Your Demeanor
Grainne Mhaol
Killybegs (From The Chieftains "Long Black Veil"
Lovely Rose Of Clare
O'carolan Tribute
Paddy's Night Out
The Bold Fenian Men
The Celtic Symphony
The Charladies Ball
The Devil And The Bailiff The Hiring Fair
The Irish Brigade Or Battle Eve Of The Brigade
The Old Man
The Widow's Walk^^
This Little Place Called Ireland^^
Trip To Jerusalem
Weave And Mend
When New York Was Irish