Carthage's actual unit roster from their own regions should only contain Libyan, Liby-Phoenician, and Citizen troops. The actual difference between Liby-Phoenician troops and Libyan troops is... uncertain, but it's extremely highly probable that there was no difference at all; they lived on the same land, fought the same foes, were practically the same people, so were likely armed and fought in the same manner; I don't think it's necessary to differentiate between them, even though contemporary authors (like Polybius) did, but this might just have been from their ethnical (therefore, their racial appearance) difference, and nothing more (more Phoenician in appearance, rather than native North African, although both seemed to dress the same anyway).
When citizens did fight, they apparently fought with great valor and zeal, but as you've pointed out, this was very rarely and usually in home defense only. There was a sacred band unit comprised of citizens, but this disappeared before the beginning of the 3rd C BCE (after been destroyed 3 times); might be exciting to include these guys as a future tech, like, "re-militarisation of the citizens"... or something like that

Other citizens, such as the nobility willing to fight in the wars, would likely have formed a type of bodyguard cavalry unit for the general, any other citizen cavalry corps is unlikely (again, apart from the sacred band, which used chariots most the time... but by the time the chariot went out of fashion in Carthage, the Sacred Band was destroyed, so if they continued to serve, they would likely have owned Elephant corps, or a professional cavalry corps... if). Citizens also served as officers and generals, and most notably, their commitment was mostly occupied with the national navy.
The reason why Carthage didn't have the usual Levy of adequately armed citizens that formed Roman and Hellenic armies, is because their farmland wasn't owned by independent farmers, but it was covered with very large agricultural estates, owned by the nobles, and worked by harshly treated Libyan slaves. Perhaps a juicy piece of info for you Magnar
If citizens fought, they would have been served as classical-style hoplites with argive shields (though depicted with slightly shorter spears than Greek ones, about the height of the user, and also larger aspis shields); as is the same for the Libyan and Liby-Phoenician levy of their land (that actually fought as heavies). Light troops (Libyans, citizens would never serve as lights, and probably not even in emergencies, because Carthage stock piled weapons and armour in the state arsenal, and would equip the levy with that) would have fought in the native style, with wicker and hide shields, javelins, and probably a melee weapon (like a short sword). Archers and slingers are unlikely, but seems as the Numidians fought in these styles (sometimes... rarely, and not at the beginning of our period), I suppose it's possible too (though I wouldn't recommend a unit for it anyway...).
It's hard to say exactly what the citizen cavalry would have fought like... I'd suggest the native, classical Greeko-Italian style, shielded, a spear (not long xyston, but relatively long spear, like the Roman equites' style), a sword, heavily armoured, and perhaps a couple javelins(?). I DON'T recommend horse armour in any form. Same style for the Libyan and Liby-Phoenician units I suppose, though I doubt either would be able to serve in a cavalry corps...
Numidian's and North Africans (as you put it, or the Moors and Gaetuli) were strictly Allied troops, and not Levied from Carthage's own lands, and this should be represented properly.
Hope that helped Magnar
