You know, it did. It's called Vatican.

(I assume you were talking about the Papal States, right? Though it is actually pre-1900 (1870 IIRC) to have it confined to Vatican only.)
As for the city of Rome, it still exists, and signed a peace treaty with the city of Carthage in 1983.
OOC:
That's the only way the question can be reasonably understood without sending it crashing off the post-1900. A good question (and maybe challenge), BTW: can what we know as Vatican achieve more territory with a post-1900 POD?
...So what, how?
January First-of-May
