These books may help:

William H.A. Williams, 'Twas Only an Irishman's Dream: The Image of Ireland and the Irish in American Popular Song Lyrics, 1800-1920 (Univ. of Illinois Press, 1996) [esp. section 2: "Romantic Irish Popular Songs in Antebellum America"]

Charles Hamm, Yesterdays: Popular Song In America (Norton, 1979) [esp. chapters 3 ("Erin, the Tear and the Smile in Thine Eyes; or, Thomas Moore's Irish Melodies in America") and 8 ("Come Back to Erin: or, More Gems from the British Isles")]

Robert R. Grimes, S.J., How Shall We Sing in a Foreign Land?: Music of Irish Catholic Immigrants in the Antebellum United States (Univ. of Notre Dame Press, 1996)

~Masato