It's a lovely poem, and I wish I could find the tune, but I searched all the ways I could think of to find it online, and I couldn't.

I think that the willow green in the song refers to some kind of clothing, and that in the time and place where the ballad was published, people understood the reference. In the first verse, she says to her lover:

"Chear up thy heart and do not fear,
    thou shalt not wear the Willow Green."


And at the end of the poem we are told:

"Where as they Married was indeed,
    now he cast off the Willow Green."

It may refer to a military uniform or perhaps a servant's livery. Whatever it means, by marrying he escapes having to wear it.

Thanks for posting, Stower.