Both per-Roman Carthage, when trade was done by Horses, or Roman Carthage which saw the slow switch to Camels do to the Sahara desert becoming dryer.
http://www.livescience.com/4180-sahara-desert-lush-populated.html
http://oceanworld.tamu.edu/resources/environment-book/desertificationinsahel.html
http://web.me.com/uriarte/Earths_Climate/11._The_Holocene.html
Horses were the preferred way to do trade, but that seems to have ended about the time of the birth of Christ do to the increase aridness of the Sahara. The Sahara before about 5000 BC was a Savannah not a desert, but from that time forward has slowly become dryer. It was still wet enough for horses till about the time of Christ, but shortly after that date it became to dry for most horse draw wagons to cross the increasingly dry desert. Camels were introduced about the time of Christ to "Solve" this problem, but apparently used for a Camel riding border guards for the first 200 years, then trade after 200 AD, but the real boom in camel usage was after the Arab Conquest after 750- AD.
Please note, some of the above comments is based on very limited historical documentation. For example, we know Carthage main source of Wealth was its trade with area around Timbuktu, but it is unclear how much of that survived the destruction of Carthage at the end of the Third Punic War. On the other hand we know the wealth was still available for Caesar re-founded Carthage about 80 years after it had been destroyed, and it quickly became the Second largest city in the Western Empire (Behind Rome itself, and behind Alexandria Egypt, if you consider the entire Roman Empire, i,e, Carthage was the third largest city, behind Rome and Alexandria).
The Arabs destroyed Carthage but its harbor had become marginal by that time and Tunis was more then able to replace it (Tunis had always been Carthage port) and again it boomed till the Portuguese found out how to said to the "Gold Coast" of Africa (Nigeria and its neighbors) and bypassing the entire trans-Sahara trade system. Once trade went by ship, Timbuktu became a back water that most people have heard of, but no one ever went to.