There is at least one song listed here called "One Morning in May" . I clicked on a link, and it wasn't the song I have in mind, so I'm not sure whether or not the following song has already been proposed.

ONE MORNING IN MAY (2)

One morning in May, as I carelessly did stray
to view the green meadows, and the lambs sport and play,
in the clear morning dew, as I lay down to muse,
a fair maiden of honour appeared in my view.

Says I, “Pretty maid, how happy we could be
for it is so ordained, love, that married we should be.
Let me not see you frown, for this heart is your own.”
But as these words were spoken, sure the tears trickled down.

“Come dry up your tears. You have nothing to fear.
I have roamed through the green fields for many’s the long year.”
But as the birds sang so sweet, this young man proved his deceit,
saying, “Adieu, pretty fair maid. We shall never more meet.”

“With my snuffbox and cane, the whole world I would range,
like Venus or Diana in search of her swain.
While the moon does shine clear, I will mourn for my dear
over mountains, clear fountains, where no-one would hear.”

“And there’s one thing I know; and that before I go.
I shall never return, love, to hear your sad woe.
And there’s another thing I know; and that before I go.
That the ranger and the stranger have many’s the foe.”

sung by Christa Burch

sung by Len Graham

discussed on a Mudcat thread