If the unification has to happen during the late Middle Ages - early Renaissance, Gian Galeazzo is the best bet by far. There might be a choice of PODs, actually: either GG is more successful and decisive in his suit for the hand of Maria of Sicily (although given the Aragonese opposition keeping Sicily under his control would not be easy, the more so since he still has to get rid of his uncle Bernabo' and his brood) or in a more simple way by avoiding his sudden death in 1402. In the latter case, GG would have the time to unify his dominions (and apparently he started to do that, unsurprisingly relying on the townspeople to keep the aristocrats in line). It is true that the Viscontis were plagued by the habit of parcelling out feudal holdings to all male heirs, but the plum that GG might be able to get would be a clear incentive to move toward a single successor.
There are other possibilities: Frederick II is the most obvious, but if we go back in time there are other possibilities to manage a unification.
My favourite is avoiding the Gothic wars and there are a lot of possibilities to do that. No Gothic wars mean that Italy would not be ravaged and it might also avoid the worst of the plague. Over the time, the Ostrogothic kingdom would stabilise, and most likely turn catholic, since the Ostrogoths would remain a definite minority. A strong Gothic kingdom would be likely to manage both the Longobard invasion on the eastern border and the Franks on the western one. It might even be able to absorb the Longobards, and keep control of the Noricum and the Dalmatian coast.
Going a bit forward in time, the success of the Pippinids is not a God-given plot, whatever the Carolingians apologists wrote ex-post facto. Given the long history of internecine wars among the Frank kingdoms, I'd say that it was quite surprising that Frankia unified, and successfully managed not only to deal with all the various troubles on their borders, but even to absorb Alania, Bavaria and eventually the Longobard kingdom of Italy. If OTL story of unmitigated successes is somehow derailed, the Longobard kings might eventally manage to curb the pretenses of the various dukes, as they almost managed before the Frank invasion, and eventually to expel the Byzantines from southern Italy.
If there is a Charles, and history goes as per OTL, Lothar might be more lucky, or able, and keep hold of both his kingdom and the imperial crown. Since the Lotharingian lands included the most developed and richest parts of Europe (although with very exposed borders) it might become a success story.
Even disposing of Lothar as per OTL, Italy was - notionally - a separate kingdom, until Otto made a grab for the imperial crown. Otto's first (and most critical) descent into Italy was greatly facilitated by Atto of Canossa, a great-grandfather of the more famous Mathilda, who not only allowed him to cross without opposition the Apennine passesm but also delivered in his hands the widow of the last king of Italy, Adelaide of Susa. Otto's marriage to Adelaide clinched the deal in terms of prestige and legitimacy (not to mention the huge swath of lands she brought as dowry): if Atto decides to hold Adelaide for the Italian claimant (whose name I don't remember right now) and closes the passes to Otto's army, it is quite possible that there is no Ottonian empire nor a German domination in Italy.
Finally (and still staying with the Canossa), if Bonifacio (Mathilda's father) is not killed in his prime during a hunt the Canossas might be the dinasty that unifies Italy. Bonifacio when he died controlled most of northern Italy, all of Tuscany and large swaths of Umbria, Marche and Abruzzi. Which gives credence to the claim that the emperor himself paid an assassin to get rid of this potential (and quite worrysome) opponent.
