Well, of course the obvious answer is to intervene early in the medieval period, when the Pope didn't really have any secular power, so that unified Italy probably ends up being his patron and it doesn't really make any sense to talk about him "summoning the Christian World to defend him" or having to take Rome or the Papal States.
Once his position is solidified and he has secular power, then he's going to act like any other secular prince, which means that he will oppose the unification of Italy by anyone other than him. But before that he doesn't really have the ability to.
Quite obviously the sooner the pope is relegated to a mostly spiritual role the better it is.
The best bet in this respect would be the Lombards, provided that there are enough trouble on other fronts to butterfly away Pepin's invasion of Italy (quite a difficult task, though).
A late-Carolingian alternative would Louis, son of Lothair. In 850 was crowned co-emperor and given government of Italy, in 863 gained the crown of Provence too. He was reasonably successful in his wars against the Saracens in southern Italy. The problem is that he had only one daughter, and upon his death he named heir Carloman, son of Louis the German. Not only did this open the door for East Frankian ambitions in Italy, but his only daughter married Boso of Provence creating another potential claimant to the Italian crown. If he had sired a son, the Carolingian dynasty of Italy would be established (and possibly Provence too would be tied to Italy for good).
Soon after Louis there was another possibility, Berengar of Friuli who gained, lost, regained the crown of Italy and in 915 was also crowned emperor. There are not huge records about his reign, and he alternated successes to defeats.
In all honesty he had to face the brunt of the Magyar invasions in the late 9th century, and that was not an easy task (his defeat at the hands of Magyars at the battle of Brenta in 899 was the spark for a conspiracy of the major Italian feudataries who deposed him for a time). Give Berengar a good victory on the Brenta river and a lot of things may change. A possible difficulty might be the fact that he also sired only two daughters. However the younger married the marquis of Ivrea, of the powerful Anscarid house and had a son (Berengar II, who later became briefly king of Italy). IOTL the obvious attempt to forge an alliance with the Anscarids failed (and his daughter Gisela died in 913). If his Magyar problems had been successfully met, I would expect that his stronger position would make the alliance more successful, in particular if his grandson Berengar were to be named heir.
So...like Rome? History repeating itself like that would be rather amusing...
As a counter-example, though, there's Rome, despite my statement above, which had a similar attitude about citizens for a long while yet conquered Italy anyways, with legal distinctions between citizens of Rome and inhabitants of other Italian cities persisting until the Social War. Surely if Athens somehow managed to reduce the other cities of Greece to being dependent allies (like most of the Delian League) or colonies (never mind that either is hugely implausible for the moment), then we would now regard it as having "conquered" Greece, even if it wasn't directly ruling most of the country?
Well Rome too has some similarities with Venice, but also huge differences. Just to name a few, Rome had a bigger population base than Venice, was always a land power and with time managed to change substantially its relation with the neighboring peoples (at least after the Social Wars). Venice was mistress of Veneto, Eastern Lombardy and Friuli for 4 centuries but the issue of fully integrating the inhabitants of these areas (who spoke a very similar languages and had always been faithful to their oath to the Republic) was never discussed, much less considered an issue.
I would say that this is a behavior resembling the Athenian one, rather than the Roman.
