arrrrrghh, now those are the most annoying! personally I often auto_win those - tho often enough I refight them as autowin often has much more causualties and almost never kills the enemy FM. but what was his army composition? full of elites? levy only or regular army? did the carthagians sent elephants against you already - In my campaign carthagians only had one unit of elephants left when I came which WAS the garrison of the westernmost settlement on sicily and I autoresolved it because I was sick of siege battles for a while^^
Yeah prodromoi are very good medium cavalry, can run around for houres, also usefull for charging!

the thing i remember best about battleing carthage was that Kyrene got attacked all the time by huge stacks(from both sides) which resulted in me garrisoning a fullstack + a avant garde made out of cavalry in/in front of it. It was a good idea to destroy the recruitment centers as that took out the feenemkin which really are dangerous when on walls. oh and the siege engines

I actually had it quitte stable a year ago, gotto look into that in more detail.