Steve,
This is the one I remember

The water is wide, I cannot swim over,
And neither have I wings to fly.
Give me a boat that can carry two,
And both shall cross, my love and I

A ship there is and it sails the sea,
It's loaded deep as deep can be.
But not as deep as the love I'm in,
And I can neither sing nor swim

Oh waly, waly, love is bonny
And it is a joy when it is new.
When love is old it waxes cold
And fades away like the morning dew.

(sorry for the garble - always the same before breakfast)

I've always known this as Waly Waly, though I agree entirely with your 'floater' comment - the Journal version seems to be 2 floater verses and a refrain.
I can see some connection with the somewhat enigmatic 'Carrickfergus', but no more than a 'floater' one

The Journal article (the paper given by Kidson) leaves the impression (though it is by no means clear) that the sung examples are by Society members
Jim Carroll