I'm not sure how 'Mo bhron ar an bhFarraige' comes to be Connie's song but that translation is rather too free for my taste. This is what I get from Hyde's book.

My grief on the sea!
How the waves of it roll!
For they heave between me
And the love of my soul!

Abandoned, forsaken,
To grief and to care,
Will the sea ever waken
Relief from despair?

Were I and my darling,
(Oh, heart-bitter wound!)
But on board of the ship
For America bound.

Oh my grief, and my trouble!
Would he and I were
In the province of Leinster,
Or county of Clare.

On a green bed of rushes
All last night I lay,
And I flung it abroad
With the heat of the day.

And my love came behind me,
He came from the south;
His breast to my bosom,
His mouth to my mouth.