Here's the lyrics from the Folkways album liner notes (link):

Beyond the obvious original source of this text there is little else that can be said of it with certainty. It is doubtful that the Biblical tale was merely set to music as an aid to memory, and it has been suggested that it is perhaps a political satire which at some date had allegorical significance. If so, the satirist and his intended victim remain anonymous.

When father Adam first did flee,
  From presence of the Lord his face,
His clothes were short, scarce covered his knee,
They cryit God pitie and hald him in chaiss.
Stay Adam, stay Adam saith the Lord;
Where are thou Adam, turn thee and stay.
"I was afraid to hear thy voice and
  naked thus to come in thy way."
"Who hast revealed to the,
  that naked thou shouldst be?
Or hast thou eaten of the tree!?
  Which I commanded thee
It touched should not be,
  therefore beginneth thy misery!"
Oh Adam, oh Adam, I pity thee.

Away went Satan maist discontent,
  Christ being promised for tae ring
For he could not have his intent,
  for power of that almighty king.
Our freedom, Lord, we have from Thee,
  that bowls of mercy poured out
Upon Thy whole posterity of thy free
  grace withouten doubt.
Therefore we all humbly entreat Thy Majesty
  that we may ever thankful be.
And for our sins contrite praying to thee most sweet
Dear Jesus, have pity on me.
Oh Adam, oh Adam, I pity thee.

I'll try seeing if I can see anything formal on the origins, but I can't think of why the assumption of the author of the liner notes (that no one would set the story to music) would be valid; people will write a song about anything -- or at least time seems that way sometimes.