Fiddler's Green refers to both the sailor's and cavalry's paradise. The OED2 has a citation from 1825 as the sailor's paradise. Common usage also seems to hold this view (John Connally [Ireland] song from circa 1960, Stereophonics [Welsh Band] song from late 1990's). I know this reference is not American, but I am also not sure if it originates from Ireland, Scotland, or England.
The cavalry paradise reference seems to come from an anonymous poem published in the Cavalry Journal in 1923 and associated with the 7th U.S. Cavalry from the post-Civil War era and the Indian Wars period (circa 1860-1870). Fiddler's Green is listed sometimes as a poem and other times as a cavalry prayer. Now, there is a link between the 7th U.S. Cavalry and Ireland. Many troopers of the 7th Cavalry were of Irish origin, and the 7th Cavalry's own insignia has the phrase "Garry Owen" on it. "Garry Owen" is a derivative of the Irish Gaelic Garraí Eóin which means Owen's Garden. Owen's Garden was a commons in Limerick that gave rise to a drinking ballad of the same name. The 5th Royal Irish Lances, an Irish cavalry unit, used that drinking ballad. I have no evidence that the Irish Lancers appropriated the paradise and incorporated it into a poem that emigrated to the U.S. with its members, or whether the paradise and poem are of U.S. origin. I am also assuming (but it seems a sound assumption) that the reference for Fiddler's Green as a sailor's paradise is the original, although I have no direct evidence of that either.
"Since the 19th century, British sailors have called the traditional heaven of mariners Fiddler's Green, 'a place of unlimited rum and tobacco.' "From the "Encyclopedia of Word and Phrase Origins" by Robert Hendrickson (Facts on File, New York, 1997).
"Old seamen are such notorious yarn spinners that it is difficult to know which of their stories to believe about Fiddler's Green. Some say that an old salt who is tired of seagoing should walk inland with an oar over his shoulder. When he come to a pretty little village deep in the country, and people ask him what he is carrying, he will know he has found Fiddler's Green. The people give him a seat in the sun outside the village inn, with a glass of grog that refills itself every time he drains the last drop and a pipe forever smoking with fragrant tobacco. From then onwards he has nothing to do but enjoy his glass and pipe, and watch the maidens dancing to the music of a fiddler on the village green.
Other sailors say that Fiddler's Green lies at the back of the trade winds in the South Atlantic. It is a stretch of water forever calm, and green as the eyes of a mermaid, where the spirits of old ships and seamen find eternal anchorage. As the sun goes down, the strains of a fiddler float across the waters and the seamen dance hornpipes upon the tranquil sea.