I was reminded of this song, which was around back in the 1960s, posted on this thread
to see if anyone else remembered it, and, by the wonder of the 'cat, a few hours later, there it was, together with the names of others who had sung it (David Campbell and Hamish Imlach).

One Day Old (Langston Hughes / (Archie?) Fisher)

Hush little baby, don't be forlorn
Though you were lynched before you were born
Your skin is black so it's understood
Though you're one day old you're no damn good

Hush my baby, though you're right to bawl
Your skin will creep before you can crawl
You'll live just as long as some people think you should
For you're one day old and no damn good

Some day you may be the President
And have the White House for your residence
So dry your tears and don't you frown
The rope and the whip can't keep you down

This nightmare, baby, can't last the night
We'll end it soon, the black and the white
We'll mark its grave with a cross of wood
Saying, One day old and no damn good

(I've done a bit of a tidy-up on the lyrics, based on listening to my almost worn-out sleeveless copy of Paul McNeil's LP, which I rooted out from the depths of my mathoms closet!)

Alan