The Bishop of Rome had significant temporal power from at least Pope Miltiades, a trend that generally accelerated (with interruptions, Byzantine and otherwise) until the papal domains assembled its own navy to combat Muslim invaders in 849. The Popes intermittently maintained naval forces in addition to armies in the centuries that followed.
Starting in the 1840s, the gradual unification of Italy squeezed the Papal States and its armed forces. The last warship serving in the Papal Navy (Marina Pontifica) was a screw corvette built by the British in 1859 and named the Immacolata Concezione. According to a 1963 article in the US Naval Institute's Proceedings, it had 8 18-pound cannons and a very comfortable cabin built with the Pope's travel in mind. The crew of 46, though, was primarily tasked with protecting the Papal States' fishing rights.
In 1870, the Kingdom of Italy invaded the Papal States and, erm, persuaded Pope Pius IX that the temporal power of the Bishops of Rome had reached a conclusion. The Immacolata Concezione was integrated into the Royal Italian Navy. It later entered French service. The precise fate of the vessel is uncertain, but it was definitely the last warship to sail under the Papal ensign.