It's noteworthy that the economy of Carthage rebounded fairly well after it's defeat in the second Punic war. Once Rome had wrested control of the Mediterranean from Carthage, the city could focus on mercantile matters rather than imperialistic matters. This, of course annoyed Rome to no end.
Let us suppose a situation in which this happy state of affairs for Carthage continues. Perhaps they are allowed to remain as a strictly Mercantile city state by Rome. Perhaps they are more peacefully subdued by Rome or anither expansionist power such as Alexander's empire. In my current timeline, I have Carthage peacefully taken under Rome's wing and treated to the same liberty's as your typical Italian city.
Regardless of what happened specifically, what might we see from this Carthage? Would they continue to simply ply the trade routes of the Western Mediterranean? Might they attempt to found colonies wherever possible? Might they venture once more out onto the Atlantic coast?