In truth, Pius XII had at least one according to a Time magazine report I stumbled across from 1944. It says the Vatican had:
Mobilized a "special defense corps" estimated at 2,000 men to guard Vatican property in Rome.
Acquired a fleet of 21 coastal ships to bring food to the "hard-pressed people of Rome and Vatican City." The ships will operate between Rome and Genoa, flying the Vatican flag.†
Other defense measures taken during the past six months: 1) increase of the efficient, well-equipped Swiss Guards from 100 to 600 men; 2) increase of the Pontifical Military Guard (papal gendarmes, who ordinarily police palace and gardens) from 800 to 3,300 men; 3) quadrupling the Palatine Guard of Honor to 2,000 men. This small army has been equipped with modern weapons. The Vatican walls have been prepared for machine-gun defense "should the occasion arise."
†The small Vatican flag has two equal vertical stripes, yellow and white, carries the papal insignia. Until 1860 the Vatican had a small armed navy, used chiefly against pirates. (AWESOME!! VATICAN NAVY VS. PIRATES!!)
I couldn't find too many photos of these soldiers online, all but the Swiss Guard were abolished by Paul VI in 1970 (oh brother) so here are some for you (click for a larger view):
The Papal Gendarmes (being inspected by Charles de Gaulle:
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The Noble Guard (as the name suggests made up of only Noblemen) they were also a horse guard I believe:
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The Palatine Guard, the main body of the Pope's forces, all volunteers:
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and of course, the Swiss guard:
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