This version is from the GEST Website of Newfoundland songs. I don't completely understand their explanation of where this particular variant came from.

My Dear Mary Anne

Oh, fare thee well, my dear Mary Anne,
Our days have all gone by;
Spring is coming, and soon I'll be gone,
But, I'll come back, don't you cry, my dear Mary Anne.

A lobster dies in the boiling pot,
Oh, pity the bluefish, too;
But, they're quickly gone and they suffer not,
The way I cry for you, my dear Mary Anne.

Oh, fare thee well, my dear Mary Anne,
Our days have all gone by;
Spring is coming, and soon I'll be gone,
But, I'll come back, don't you cry, my dear Mary Anne.

Oh, don't you see the pretty turtle dove,
That flies from pine to pine;
Crying for its own true love,
The way I cry for you, my dear Mary Anne.

Oh, fare thee well, my dear Mary Anne,
Our days have all gone by;
Spring is coming, and soon I'll be gone,
But, I'll come back, don't you cry, my dear Mary Anne.

####.... Author unknown. Variant of a 19th century British broadside ballad, My Mary Ann, published by W.S. Forley (London) sometime between 1858 and 1885, and archived at the Bodleian Library Broadside Ballads, shelfmark: Firth c.12(366) ....####
A variant was published as #48, Mary Ann, by Edith Fowke (editor) with Keith MacMillan (music consultant) in The Penguin Book of Canadian Folk Songs, (1973). A variant was also recorded by Ian and Sylvia as Mary Ann/Anne, on Ian & Sylvia, (Vanguard Records VSD 2113, LP, 1962, cut #A.06.

Source: http://www.wtv-zone.com/phyrst/audio/nfld/07/maryanne.htm