The problem is that even postulating a mediterranean-oriented Moslem state, the feasible invasion routes to Italy are just 2: across the straits of Otranto (lower Adriatic) or across the channel of Sicily.
Otranto has the problem that lower Adriatic is not so easy to negotiate in winter (and also spring/autumns are not really easy for the ships of this age).
OTL, Mehmet II (if I'm not wrong) sieged and took the city of Otranto, and kept it for a few years. There was never a real effort to convert this beach-head into the basis for an invasion of Italy (and the logistics would have been a nightmare, without a complete dominion of the sea). The lower Dalmatian coast is a maze of channels and islands (and was pirate heaven for thousand of years): I can imagine Venetian, Neapolitan and papal galley attacking the supply convoys from here, from Corfu and from Taranto.
The channel of Sicily is even more difficult (we are talking of late Middle Ages, and of transporting a major army, with supply train, to Sicily). Additionally, in this period Tunis cannot supply a lot of food stuff (the African bread-basket has been gone for centuries). By comparison, remember that the Arab invasion in 827 consisted of a few thousand warriors only, and they were invited by the Byzantine governor of the island, and given the town of Milazzo for their own.
I'm afraid I must stay with my opinion: if you want to invade Italy, you do it the usual way, from NW or NE, and move downward. Or you can try a naval landing in Sicily (like the Aragonese did) if you have a party on the island supporting you.