There was a music hall song written, I believe, by Harrigan & Hart that goes something like...
St. Patrick was a gentleman his name we celebrate
And on the 17th of March the Irish congregate
With a brand new hat on each man's head,
A green necktie that's newly made,
It's right foot first and lightly tread
In the Patrick's Day parade.
And it's 2 by 2 away we go
Up Sackville Street in rain or snow
We'll face the devil friend or foe
In the Patick's Day parade.
Let me know if this is the one. I have the words on sheet music and also in a book. Both are in storage. I'll pick them up and type out the rest of the words if you'd like them.
Sackville Street was renamed O'Connell Street (Dublin's main street) after the Revolution. I believe the Harrigan & Hart original probably used "Broadway."
All the best,