ANSWER: My quick answer is that I cannot be certain whether our Savior was black or not. This is because the Bible gives us almost NO physical description of Jesus. Our Savior, the God who became a man, was a Jew and a member of the tribe of Judah. He was a descendant of David, King of Israel, who was described by the prophet Samuel as not being dark skinned but looking "ruddy," meaning red or reddish color.
And Samuel said to Jesse, 'Are all the young men here?' Then he said, 'There remains yet the youngest, and there he is, keeping the sheep.' And Samuel said to Jesse, 'Send and bring him. For we will not sit down till he comes here.'
Now he was ruddy [Hebrew: 'admôniy, Strong's Concordance Number #H132, meaning "reddish of the hair or complexion"], with bright eyes, and good-looking. (1Samuel 16:11 - 12)
Note also that this ancestor of Jesus had "bright eyes, and good-looking," although having beautiful ancestors is certainly no guarantee of how a person looks. Although he doesn't mention him being any particular skin color like black, Isaiah does give us a general description of his physical appearance.
2 It was the will of the Lord that his servant grow like a plant taking root in dry ground. He had no dignity or beauty to make us take notice of him. There was nothing attractive about him, nothing that would draw us to him. (Isaiah 53:2)
One formerly well-known religious author and preacher (who is now dead) wrote concerning what he thought our Savior likely looked like. He believed he was of average height for his time. Additionally, because of Jesus' hard work of helping his physical father in the carpentry business, he was likely thinner rather than fat and had the kind of muscles conditioned by hours of pushing, tugging, moving, pulling and other activities required of his occupation. In short, he looked like any other person born of the tribe of Judah who lived in Palestine during the first century A.D.
Considering the Biblical description and racial characteristics given us by secular history, the evidence points to the fact that Jesus was not black or African in ancestry or looks. The important thing is that, no matter WHAT he looked like or what color was His skin, or what texture was His hair, or what shape His physical features took, He was God, the Son of God, and our Lord and Savior and He remains the only path to salvation for man.