A possible good POD might be Gian Galeazzo Visconti surviving his fever bout in 1402 to conquer Florence and Bologna. He would have quickly united all of Italy north of Rome in one big kingdom. IRRC, he had plans to get oneself crowned as King of Italy by the Holy Roman Emperor after Florence fell, when he died.
I like this POD. By getting Italy united in the opening years of the 15th century, you can have Italy unite itself during this century, and hopefully avoid becoming the cockpit that it was by the end of the 15th century.
The problem that this is going to run into is that the HRE was loath to hand out crowns (just ask Duke Charles the Bold of Burgundy). The Holy Roman Emperor probably isn't going to give out crowns, so then Mr. Visconti will have to find someone else with the power to conjure crowns.
A better place to go might be the Pope. The Pope in the past had given various bits of Europe to crowned heads (Ireland to Henry II comes to mind), and I believe that the Norman Kingdom of Sicily was a Papal vassal (for as long as it suited the Sicilian Normans).
So perhaps Mr. Visconti, having conquered Bolonga and Florence, decides to revive the Iron Crown of the Lombards. In order to have this recognized by the other crowned heads of Europe, Visconti contracts the Pope (whom he probably caused to be elected, or caused to become wealthy, pick one) to give him the Iron Crown. The Kingdom of Lombardy is a historic title, and Visconti can concoct a lineage that shows him related to the last Lombard King or something.
Once you give Visconti his kingdom however, the next problem you'll have to face is succession. If he lives longer, then perhaps one of his sons becomes strong enough to ensure a peaceful successsion, but short of killing the other heirs (and I wouldn't put that past Gian Maria Visconti) I don't think a peaceful succession happens. Now perhaps with the Kingdom the other heirs are now clearly not equals and they fall in line, with strong armies of their own, united in name under Lombardy, but not in fact.
Once the Iron Crown is revived, and encompasses the large areas that it does (Milan, Florence, Bologna), I think that it is likely that another person could use this recent event to justify another conquest.
I'm thinking that if we have a Hapsburg like family arise (not the Hapsburgs per se, but another Europe-spanning familial empire) then one of their possessions could be Lombardy. Basically, once the crown is revived, you've made those three cities part of the same package, so that even if Italy still turns into the cockpit of Europe, the prize will be the Kingdom of Lombardy, rather than arbitarily drawn lines on an map of northern Italy.