The timeline gets interesting here.
Papal States Join the Triple Alliance
By 1882, Italy in real world joins the Triple Alliance with Germany and Austria-Hungary. Assuming there is a two-state solution that agrees somewhat on foreign affairs, Papal States would join as well.
Industrialization was under way in Italy during the late 1800s and early 1900s. The Papal States would need to have a progressive Pope, willing to pursue fast modernization of economics to survive. This is possible to do in an authoritarian environment. Ask the German Empire, they'll tell you how.
Papal States Ideology - Stronger than Nationalism
As the north of Italy industrializes, there would need to be charismatic Popes and social movements creating some religious-nationalistic identity for the Papal states. Tapping into Ultramontanism. Recruiting fervent Catholics to serve the Pope. Creating a politically and economically progressive ideology that upholds the complete authority of the Pope, for the glory of God and the universal Catholic church. Perhaps even disaffected Catholics fleeing the anti-clerical policies in France in the late 1800s and early 1900s.
The Great War
The Papal States stay neutral during World War I, along with Switzerland. Perhaps the Kingdom of Italy also stays neutral. This is where the butterflies begin to spin out of control. World War I was such a pivotal moment in history, you could take it 50 different ways.
For example: Germany wins in 1917 after the Russian Revolution-- without the pressure from Italy in the south against the Austro-Hungarian Empire, they barely roll over the trenches and take out Paris. 274
France is humiliated and signs a peace deal. Italy and the Papal states decide that authoritarianism wins, and doubles down on dictatorship. Fascism in the Kingdom of Italy, and an equally nasty Papal authoritarianism in the north. <PERSON> all around. Embracing Catholic supremacy, much like the Austrians during that same time.
The Next Great War
Another war would inevitably explode with a Revanchist France and an over-bloated Germany and the expanding Communist Russia. What happens next creates even more butterflies that could go 100 different ways.
Perhaps the Papal States stay neutral, like Switzerland. To appease the religious Austrians, the Germanic allies decide to leave the Papal states alone. Perhaps the Papal states are enthusiastic about the German militarism against the godless communists of the Soviet Union.
Dictatorship into the 21st Century
Regardless, it is very possible for authoritarian states to survive deep into the 20th century in Western Europe. Look at <PERSON> in Spain. Look at Portugal. Those semi-fascist authoritarian governments, with heavy Catholic religious support, continued far into the 1970s. Savvy popes could very well do the same all the way into the 1980s.
After that, it gets tough. Either Germany would have to win and spread authoritarianism through the continent (in which case France and the Kingdom/Republic of Italy also remain authoritarian), or the Papal state in the 1980s and 1990s would turn inward, becoming a regressive dictatorship like Belarus-- which to this day is an authoritarian government sitting strong in Europe. 274