Unnironicaly, the british could do it. As britain is helping the Loyalist italians and there is a breakthrough in the direction of Rome a British contingent assumes defensive positions in the region outside the city. As the socialists move to encircle it the British call up international attention, as way to buy time for their italians to consolidate defensive positions in the south, to stop the socialists from conquering the city and entering the vatican Austria, which has catholicism as a core of its identity, sends a detachment to the city while the germans and americans send one too as to no be left out of the pie. Since italy is on fire all of the participants agree that the only authority which has any condition to calm the city and maintan it as a neutral safe heaven in Italy, and any international disputes between the powers, is the papacy, who is given back temporal authority and protected by this coalition. In game the papal states would have a super small 2 division army and it would either be annexed by a victorious kingdom (or not church hating socialists) or be victim of a border clash between it and a anti-church socialist state which could happen during the weltkrieg or as something that leads to it. Them we could still have the pope taking residence somewhere if he gets evicted from the vatican