The best part about your question is that the Cothon, that is the circular, dug out military part of Carthage's harbour, still exists and can be visited in Tunisia^1. An interesting paper on this practice (circular dug out artificial harbours) was published in 2005 in Méditerrannée by N. Carayon^2, where he identifies other such harbours in 6 other places in the Mediterranean. Stager^3 dates the rectangular port (at least some of its features) to the late IVth or IIIrd century, and Hurst^4 dates the circular harbour to the middle of the IInd century BC (which is very late as far as Carthaginian history goes). This does not exclude an older, preexisting military harbour which could have been a Cothon but definitely dates the last major overhaul of this site as posterior to the second Punic war.

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^1 : Well, could be visited back when I was a teenager and Tunisia was stable enough for tourism

^2 : Le cothon ou port artificiel creusé. Essai de définition, N. Carayon, Méditerrannée, n.1.2, 2005

^3 : Stager L.E., (1992), Le tophet et le port commercial, in ENNABLI A. (dir.), Pour sauver Carthage, exploration et conservation de la cité punique, romaine et byzantine, UNESCO/INAA, Paris-Tunis, p. 73-78.

^4 : Hurst H., (1993) Le port militaire de Carthage, Les dossiers d’Archéologie, vol. 183, p. 42-51