"In the year of our Lord eighteen hundred and four There was great rejoicing round Erin's green shore, When Daniel O'Connell he made this appeal: 'All I want is fair justice to gain my repeal.'"
The current description is all of the Creighton-SNewBrunswick fragment.
See also Bodleian, 2806 c.15(195), "Erin's Green Linnet ("On a fair summer's morning as day was just dawning"); Harding B 19(39), "The Green Linnet"
Daniel O'Connell (1775-1847) tried to convince the British to reform administration of Ireland and was the leading figure on behalf of Catholic Emancipation. (For his history, see also "Erin's Green Shore" [Laws Q27]).
Creighton-SNewBrunswick: "Our solitary stanza may refer to the Tithe War." That may be but does not tie in with 1804. O'Connell's Catholic Association was formed in 1823 to resist the requirement that Irish Catholics pay tithes to the Anglican Church of Ireland. The "war" was passive for most of the period 1823-1836, though there were violent incidents in 1831 (source: _The Irish Tithe War 1831_ at the OnWar.com site) - BS
I am more inclined to accept the date than Creighton's explanation. O'Connell first came to prominence at the time of the 1800 Union of Ireland and England: He opposed it. (Quite reasonably, since Ireland had had a real parliament and significant self-rule under the old constitution which Union replaced.)
The name of the anti-Union movement? "Repeal."
The notion of Repeal became more of a platform in 1832, when O'Connell formed a party in parliament for the purpose. But he had been talking about the notion for decades. The date 1804 makes some sense, because it was the last year in which his primary issue was avoiding Union; starting in 1805 and for many years after, his chief demand was Catholic "emancipation" (read, essentially, enfranchisement, though it's a lot more complicated than that).
Healy-OISBv2 includes a very large section of O'Connell pieces (roughly p. 85-101, plus a few others). Few of these show any hints of being traditional. - RBW