Perhaps you can sneak in two of my favorites. (I'll use any excuse to use these melodies.)

1. The Water is Wide

I leaned my back against an oak
Thinking it was a trusty tree
But first it bent and then it broke
So did my love prove false to me

2. Turtle Dove

Oh don't you see that little turtle dove
In yonder mulberry tree?

and a related song, The Storms are on the Ocean

See that lonesome turtle dove
As he flies from pine to pine.
He's mourning for his own true love
Just the way I mourn for mine.

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How about these lyrics to Tom Dooley...

This time tomorrow, reckon where I'd be
In some lonesome valley, hangin' on a white oak tree

Or this reference to a willow tree...
There is a Tavern in the Town

I'll hang my harp on the weeping willow tree,
And may the world go well with thee.