Black and white are the predominant colors in this poem, but we can't forget the color blue—as in the blues, blues poetry, and the bruises on the lover's body. But blackness in this poem is more than a color—it's a cause of death.
Title: The girl who is singing this song is dark. This is an interesting word choice, because not only does the word "dark" denote her skin color, but implies that, after this tragedy, she's feeling very dark inside.
Lines 1, 5 and 9: This refrain, which is repeated at the beginning of every stanza, does not mention color specifically, but puts us in a place where the color of your skin can have life or death stakes: the post Civil War South.
Line 3: The color black is emphasized by its placement in the line. The rhythm emphasizes the word black, rather than the word young. The young man, we can presume from the historical context, was killed because he was black.
Line 7: Here, we see the color white. Just like our speaker emphasizes her lover's blackness, she emphasizes Jesus' whiteness. Both of them are victims—her husband hanged from a tree, Jesus nailed to a cross. But no one is making a martyr out of this young black man—except, maybe, the speaker and readers of this poem.