They were more likely to be fairer skin. Carthage was founded as a Phoenician colony and the Phoenicians themselves were a Semitic people. The region that they settled (modern Tunisia) was populated by Libyans who bear more resemblance to modern day Berbers (group of people dispersed across much North Africa). In other words they probably had a more stereotypical "Mediterranean" or even "Middle Eastern" appearance than black. It's possible that there were "black" Carthaginians because the cosmopolitan/mercantile nature of the city connected it with peoples across the ancient world, including other parts of Africa.

Good question. Maybe you can x-post this to an anthropology subreddit as well? (/r/askanthropology)