Rounder CD 1087 "From Galway to Dublin (Early Recordings of Traditional Irish Music)" contains "My Darlin' Coleen Bawn" sung by Paddy Beades--probably the same as the second song in your list. Here are the lyrics from the liner notes:

In the golden vales of Limerick beside the Shannon stream
There dwells a maid that holds me heart and haunts me like a dream
Her silky locks of golden hair, as gentle as the fawn
With cheeks to make the red rose pale, my darlin' coleen bawn.

I seldom go up to speak to her but I think of her with pride
For six long months I courted her, I thought she'd be my bride
Six weary months of cold and wet, alas from me she was drawn
I was but a poor laboring boy, she was my coleen bawn.

To leave old Ireland miles behind, it oft runs in my mind
To wander far and other brides in countries for to find
But I have seen some other lads upon her footsteps fall
That leaves me hear to guard me dear, me own dear coleen bawn.

The women of Limerick take the sway throughout old Erin's Isle
They fought within the city walls in days that's long gone by
They kept away the enemy for six nights until the dawn
Most worthy of this title was my darlin' coleen bawn.

More information from the liner notes:
Its melody is similar to those of "The Wild Colonial Boy" and "The Boston Burglar."

The forth verse refers to the siege of Limerick by the Williamite forces, when women took part in the defense of the city under General Patrick Sarsfield. Following their surrender and the signing of the treaty of Limerick in 1691, Sarsfield and his troops sailed for France, joining in exile James Stuart and thousands of Irishmen who would become known in story and song as the Wild Geese.