Hrm.... That makes a certain amount of sense, though it'd be best to keep in mind that the Vatican's government is very recent and both have been shaped to some degree in reaction to events around them. The institutions put in place to reform would not likely match the ones put up retroactively by remnant states in OTL.
So. John XXIII.
Under his reign, the Papal States enact a national land survey, just as Sardinia-Piedmont was doing. This sorts out what land is being held illegally, and what useful land is being left unused. It actually works better for the Papacy than for that northern kingdom, because an enormous amount of land falls into those categories.
Otherwise, the early years of John XXIII's papacy parallel the reign of Ferdinand II in the Two Sicilies, crowned a year earlier. A part of the money from the land reforms goes to efforts to gradually industrialize. Local industries are encouraged and a (slow) start made on a railroad to stretch between Rome and Bologna. There's a limit to how much can be accomplished in this way. Foreign competition is partly dealt with by tariff barriers (he's not a perfect liberal), but there's little cure for the utter lack of local markets.
Like much of Italy the Papal States have actually gotten poorer since the Renaissance, but the problem is particularly severe there. The church does a sterling job feeding the poverty stricken masses under its care. Unfortunately, a fair part of the origin of that poverty is in the fact that in, an agrarian economy, the church owns much of the best available land. Even as things improve there aren't many to buy the products of the first factories.
It doesn't help matters that part of John's idea of moderating liberalism includes keeping it from ruining the cities. The first few major manufactories under the papal domains are set up well outside and downwind of population centers. That's all very well and good for the tourists and pilgrims, but it makes the process that little bit more difficult.
Ideally, our good pope would like to set up some sort of representative body for his domains, but in the 1830s there's a limit to what he can do - the Church is a very conservative organization. Not that they'd necessarily refuse him outright, but incomplete compliance and procrastination will do the job just as well if he forces the issue. And he knows it. He's already being called "the banker-pope" by his detractors. In the meantime, he contents himself by exhorting the monarchs of Europe to live up to his example and by distributing land turned up by his reforms.
Ironically, the opposition to his policies actually makes the latter more successful. Rather than dividing everything equally among the poor - which would leave the average family with a smallish amount of land but no livestock, seed, or tools - he is stuck giving it out in increments. Those who do get new land get a fair amount and often some basic necessities to work it as well. Most are able to maintain the land they get without going straight into debt.
All in all, John XXIII is a popular man when 1848 comes around.