There is much evidence to argue that the Carthaginian Senate contributed as much to its defeat in the Punic Wars as did the Romans. Their senate purposefully withheld resupply and reinforcements from Hannibal Barca while on his famous campaign through Italy. What if the Carthaginian Republic was replaced by a monarchy under the Barcid Dynasty. With a unified strategy and the availability of the Empire's entire resources, could Hannibal have defeated Rome and established Carthage as the preeminent power in the Mediterranean?
I see the most likely POD as being a coup d'etat led by Hannibal's father Hamilcar Barca following the Mercenary War. Popular discontent aimed at the senate for their misconduct during the First Punic War and their inability to handle the mercenary crisis would allow Hamilcar, backed by his loyal and victorious army, to march on Carthage itself and reorganize its government. What sort of institutional changes would have to be made to enable Hamilcar, Hannibal and their successors to forge a stronger Carthaginian Empire? Could this involve adopting Roman style emergency conscription for citizens? Abolishing child sacrifice? The complete annihilation of the senate?