All due credit to ScipioAsina who quite correctly acknowledged the lack of historical sources on the topic. I have a great deal of interest in Carthage and have gathered my thoughts on the topic (drawn from reading a lot on the subject and commonsense deductions) below and I hope they will be acceptable to the mods, given the difficulty of talking about this topic.

Let's bear in mind the demographics of ancient North Africa and the Mediterranean basin in general. The worst mistake we can make is to start from modern interpretations of "black" and "white" which were different from how the Romans thought.

First off, let's look at Tunisia today. (http://4.bp.blogspot.com/_m31urYR_nYw/TT1tPApnUXI/AAAAAAAAAvw/lt6QvQwA7TQ/s1600/70686994-tunisian-people.jpg). What you should see are people who look darker than your classic whites, but bear a clear resemblance. Certainly they are different from sub-Saharan Africans. You can compare this with modern Italians as well (http://www.europeword.com/images/italy/italian-people3.jpg) and notice that there isn't too much difference between the two. Now, this certainly doesn't tell us what people living there looked like 2000+ years ago, but given the scarcity of resources its a starting point.

Now take a look at a map of the Mediterranean. Carthage really isn't that far from Rome. In fact, its more northwards than parts of Sicily. The Mediterranean basin has an (aptly named) Mediterranean climate which means that Carthaginians and Romans lived in approximately the same environmental conditions which suggests that there wouldn't have been anything to cause racial variations between the two to have been too pronounced. The working classes of both Carthage and Roman would have spent most of their time labouring outside under the same sun in pretty similar conditions. Especially back then when North Africa was more lush and less arid.

Although we don't have anything much from historical sources on the issue, we can make some deductions. The Numidians and other North Africans are depicted by Livy in The War Against Hannibal as being darker than normal but are seen as distinct from the Carthaginians. It seems unlikely that the Numidians were significantly darker (c.f. sub-Saharan Africans). Nevertheless, we know that Numidians, Carthaginians, Berbers etc must have interbred.

We also know that the Romans considered the Britons, Gauls and Germans to be very white. The failure of the Romans to devote much detail to the Carthaginian skin colour suggests that it was not considered important by the sources which Livy and Polybius drew upon. The fact that the whiteness of the Gauls and other barbarians was emphasised, but the colour of the Carthaginians was not mentioned at all, suggests that it was not worthy of remark because it was similar to the Romans.

In all likelihood the Carthaginians were not as white as someone from Britain, not as black as someone from Sub-Saharan Africa, but weren't too different from the Romans in colour. The intermixture of Carthaginians (of Semitic origin), Numidians and Berbers would have produced a ranges of skin hues, the average colour of which would probably have been slightly darker than the Romans due to African environmental conditions and Numidian and Berber blood. But the Mediterranean was (and is) a hot place, the ancient populaces spent most of the time working outside in similar conditions and were all very tanned and dark themselves.

If you'd like to see what the French think a Carthaginian looked like, check this video: https://www.youtube.com/watch?v=hL3HNg6KMpY

In reality, this is a very modern question. Today we think of white as Britain, France and black as sub-Saharan Africans. The Mediterranean civilizations of the time, such as the Romans and Carthaginians, would have seen themselves as different from both. Their skin hues lay between the two extremes.

Hello there! I apologize beforehand, as I do not have a direct answer to your question.

The average Carthaginian might have looked more or less like the average Phoenician from the same time period. What did the average Phoenician look like? I don't know! I imagine, in fact, that you would've seen a mix of skin colors. In Carthaginian ex-votos and inscriptions, we frequently find Libyan ("native") names alongside Punic ones, which suggests intermingling; and we know that prominent Carthaginian families (including Hannibal's) enjoyed ties of marriage with their Numidian ("Berber") counterparts. Ancient North Africa in general drew people from all over the Mediterranean.

That said, much of the older scholarship of Carthage (even as late as the 1990s in a few instances) did make use of racial stereotypes. To present the most blatant example, certain historians/classicists/archaeologists would refer to the Carthaginians' innate "Semitic qualities" while lamenting the negative "African influence"; not even "Hellenization" (another loaded term) could prevent their gradual "degeneration." That's nonsense, of course. There's no biological basis for race, at least not in the essentialized way it's often perceived. The topic has otherwise never come up in my research, and it doesn't make for a good historical question unless one is examining, as you suggested, modern depictions of the Carthaginians.

Kind of off topic, but Rome II certainly made everyone a good deal whiter than they probably were... because pretty much everyone in that game is northern euro white with maybe a slight coloration of the face for anyone on the south side of the Mediterranean.

Rome 1 had a more plausible race distribution. Rome II introduced real faces via mo-cap and they probably just took average Brits to do the job. Greeks and Romans are given a Northern Euro appearance, and the Romans are even given English accents. Augustus is given some kind of alien-like white spaceman appearance. Safe to say that game is up to some standard whitewashing.

I know mods may be compelled to delete this, but I just want to point the spotty historiography of the game, which may unfortunately be used as a source, or more frequently, paint a false picture of the era.

The appearance of people in Rome II is likely based on the whim of the developers.

Edit: at some point a developer made a comment saying that the game is intended to be based of of Hollywood's Rome that actual Rome.