Here is another version of the song , this is from Songs Of The Gael Part 3 published in 1921 - the author was D,A.fahy. I don't know which is the older, and I don't know of any conection between them, This version has the same tune, with an extra few words at the end of each verse.
Maybe it originated as a marching tune and evolved into songs ?.

Garryowen-Na-Glory

Oh Many a land, Once great and grand
Has bowed to foreign master
And many a fight 'gainst tyrants might
Has sunk in dire disaster
But one, I hold, creation old
One land. one cause, one story
Still lives , still glows, Still thrives and grows,
Tis Garryowen-na-glory
Tis Garryowen, our pride our own
Tis Garryowen-na-glory

By Nature blest, in verdure drest
She crests the Western waters
Oh, fairer far, than dawn-stars are
Her guileless-hearted daughters
Her bare-breast sons, have faced the guns
In many a battle gory,
Stood man to man in Valours van
For Garryowen-na-glory
For garryowen they held their own
For Garryowen-na-glory

Mavrone! the isle through fraud and guile
Has lost her olden splendour
And scattered far 'neath many a star
Are those who dare befriend her
But, mark me men, She'll rise again
Unsullied still her story
Mid freeborn lands, till peerless stands
Our Garryowen-na-glory
For Garryowen, We'll build a throne
Dear Garryowern-na-glory

Oh, many a land, now great and grand
Shall sink in stream of ages
And many a name of pride and fame
Shall fade from history's pages;
But earth shall reel at Judgements peal
In wreck and ruin hoary
Ere fades, ere dies, ere lowly lies
Our Garryowen-na-glory
Oh, Garryowen, she'll reign alone
Proud Garryowen-na-glory !

BTW Mrrzy, you are right, it was John Wayne and Maureen O'Hara. On their wedding night the cavalry officers sang the "Bold Fenian Men" I remember seeing the movie in a theatre in Belfast, it caused quite a ruckus when the song was being sung, half the audience were singing along, the other half were booing, and then the seats started to fly through the air. They removed that part from the movie whenever it was shown in the north of Ireland.