'riddle my sport' is probably a corruption. In this case the poet obviously used the term riddle as meaning to ask somebody's advice.
As Doug Wallin's splendid version had it:
'I riddle to you, my own dear mother,
And ask as your dear son.
Would you marry fair Eleanor now,
Or bring the brown girl home?'(x2)
'I riddle to you, my own dear son,
My own beloved one.
If you ask for my advice,
You'll bring the brown girl home'.(x2)
Fair Eleanor and Lord Thomas. Sung by Doug Wallin at Crane Branch, Madison County, NC. 24.5.83. From Far in the Mountains, vols 3&4. Musical Traditions. MTCD323-4.