Google Book Search finds several references to "Fiddler's Green" (the place, not the song). None of these shed any light on the origin of the term, but are interesting nonetheless. Here are some of the oldest ones:

From "The Port Admiral" by William Johnstoun N. Neale, 1833:

"... I propose we broach the rum, get thundering groggy, blow the old barky up, and all go to Davy Jones together; in which case ye see, my boys, we'll send that blue bearded beggar aloft, as pilot-boat, and make sail for Fiddler's green all standing."

From "My Life, by the author of 'Stories of Waterloo'." [by William Hamilton Maxwell], 1835:

In the kingdom of Connaught, it is universally believed that tailors and musicians after death are cantoned in a place called "Fiddler's-green." As it is not marked on any map of Arrowsmith, I cannot describe its precise situation further than that report places it unpleasantly contiguous to Pandemonium.

From "The Knickerbocker: Or, New-York Monthly Magazine," 1857:

Now Norfolk is the paradise of midshipmen, while Portsmouth, its neighbor across the river, may not inaptly be termed their 'fiddler's green;' for in both these mighty cities gold lace and gilt buttons reign supreme.

From "The Ganges and the Seine: Scenes on the Banks of Both" by Sidney Laman Blanchard, 1862:

... and the sailors and the soldiers were allowed to have their own way in such matters, for all the world as if they were on "Fiddler's Green"—to which service-paradise, indeed, many of them upon such occasions, expressed a wish to be taken, after a judicious wrapping up in a tarpauling (sic) jacket.

From "Norrie Seton; or, Driven to Sea" by Anne Jane Cupples, 1869:

"...though it's many a day since them poor chaps parted of their cable and drove away to 'Fiddler's Green,' where they has been happy with their grog, and lots o' fun; yet it don't do for a man's old carcass to be left without a bit o' burial, whatsomdever?"

"Ay," chimed in another, "who knows but 'Fiddler's Green' ain't been a quiet haven to them noways, on account of them here bones been allowed to lie without a burial."