There are only three references to color in this poem, but they serve to emphasize the division between blacks and whites in the Southern society the poem describes. The titular "dark girl" seems to be the speaker in the poem, lamenting the lynching of her "black young lover." The positioning of the adjectives here is telling: in English, our usual tendency is to put adjectives of age before adjectives of color—so, "young black lover" would be a more natural construction. In this instance, however, the fact that the girl's lover is black is what has led him to this fate. In foregrounding his blackness, the speaker draws attention to the fact that it was his blackness which defined him in the eyes of those who killed him, and his blackness which affected how he moved through the world.
The other color descriptor in the poem is applied by the girl to "white Lord Jesus." Like the descriptor of her lover, this is the third line of a stanza, meaning that parallel structures force us to see these lines as points of comparison for each other. Since Jesus is described as "white," he is drawn in opposition to the "black" lover: Jesus's whiteness here defines him, much as the lover's blackness has the same effect for him. The girl thinks of Jesus as "white" in the same breath as she asks him in despair what the use is in her prayers. The chilling effect of this is to suggest that the girl, seeing Jesus as someone who has been claimed by whites as a representative of their kind, can no longer understand how he can help black people. Jesus, in allowing the black man to be hanged, seems to be looking out only for white people, not for the blacks who are dying due to racial injustice.
Of course, Jesus was not a white man, but in imagining him as metaphorically white, the speaker has cast herself outside of his arena of concern. "White" Jesus, in a world which treats blacks in this way, seems not to care about his black children.