I don't know why, but books of old Irish songs are harder to find than books of old Scottish songs. Maybe Ireland didn't have, until recently, such a strong tradition of singing songs in English, so there were fewer songs to collect. Or maybe the songs existed, but scholars didn't bother collecting them. Or maybe scholars collected them, but Google hasn't got around to digitizing them yet. Or maybe I'm missing something.

A Treasury of Irish Poetry in the English Tongue, by Stopford Augustus Brooke, Thomas William Rolleston, 1900.

Lays and Legends of Thomond, by Michael Hogan, 1880.

Musa Pedestris: Three Centuries of Canting Songs and Slang Rhymes, by John Stephen Farmer, 1896.

Popular Songs of Ireland, by Thomas Crofton Croker, 1886.

Songs of Erinn, by Patrick Joseph McCall, 1899.

Songs of Irish Wit and Humour, by Alfred Perceval Graves, 1884.

Street Ballads, Popular Poetry, and Household Songs of Ireland, by Duncathail pseud, ed, 1865.

The Blarney Ballads, by Charles Larcom Graves, 1893.

The Cabinet of Irish Literature, by Charles Anderton Read, 1880.

The Irish Poems of Alfred Perceval Graves, by Alfred Perceval Graves, 1908.

The Lyrics of Ireland, by Samuel Lover, 1858.

The Popular Poets and Poetry of Ireland, by Richard Nagle, 1887.

The Song Lore of Ireland: Erin's Story in Music and Verse, by Redfern Mason, 1910.