Pretty interesting article, Steve. I knew there had to be nothing relating this song to Jesus- there is nothing in the hymn about caring for a baby that isn't the parent's. I'll add a similar song which although unrelated has a reversed theme:

Brown Skin Girl
(Lord Invader)

1. What's wrong with you, Miss Ivy, girl?
Why are you trying to trap me with that baby?
What's wrong with you, Miss Ivy, girl?
Why are you trying to trap me with that baby?
We only got friendly in September,
And the baby was born in November.

Girl you can't fool me like that,
Tell me how a monkey can make a cat!
(So we singin' bout)

Cho: Brown skin girl, stay home and mind baby,
Brown skin girl, stay home and mind baby.
I'm going away on a sailing boat,
And if I don't come back
Stay home and mind baby

2. Now this is something that a blind can see,
That the baby ain't belong to me,
You know that I am a fellow with a funny face,
And the baby don't belong to the Negro race.
If she go to America,
She compelled to find the right father.
So girl, don't worry with me,
You can't tie me up with that blue-eyed baby.
(chorus)

3. Yes, Ivy, girl, you made an error,
To be in love with that Yankee feller.
You thought he really come here to live,
It is better you had met a native.
You said they come here for ninety-nine years,
And they leave you with that baby shedding tears,
And now you want me to pay the tax,
Go cut down the tree where you grind your axe.
(Chorus)