I think the song Tommy Makem is parodying is this one:

GALWAY BAY
Words and music by Arthur Colahan, 1947.
As recorded by Bing Crosby, 1947.

If you ever go across the sea to Ireland,
Then maybe at the closin' of your day
You will sit and watch the moon rise over Claddagh
And watch the barefoot gossoons at their play.

Just to hear again the ripple of the trout stream,
The women in the meadows makin' hay,
And to sit beside a turf fire in the cabin,
And see the sun go down on Galway Bay.

For the breezes blowin' o'er the seas from Ireland
Are perfumed by the heather as they blow,
And the women in the upland diggin' praties
Speak a language that the strangers do not know.

For the strangers came and tried to teach us their way.
They scorned us just for bein' what we are,
But they might as well go chasin' after moonbeams
Or light a penny candle from a star.

And if there's goin' to be a life hereafter—
And faith, I'm sure there's goin' to be—
I will ask my God to let me make my heaven
In that dear land across the Irish Sea.