The Vatican Post Office sells commemorative stamps and coins for collectors, and normal stamps for mailing, in the different post offices within St. Peter’s Square:
1) to the left of the the Square (facing the Basilica) near the bookstore,
2) to the right of the Square just outside the columns (before the public toilets), and,
3) in the mobile container van on the left area of the Square.
You may also get hold of Vatican-issued 50-cent coins (only) from post offices, souvenir shops or bookstores within St. Peter’s Square. To do this, buy any item, but pay with a relatively big Euro bill. As you pay, ask them, “Do you have 50-cent Vatican coins?” In Italian, you may ask, “avete monete del Papa?” This way when they give your change, you get coins issued by the Vatican itself, with the Pope’s face on one side – rather than the usual coins issued by Italy or other European countries. Try asking for as many 50-cent coins as you want to collect or give away. Note that the Vatican circulates only their 50-cent coins; Vatican coins of other values are sold in sets as collector items, also at the Vatican Post Office, or in stores outside the Vatican, though perhaps at a higher price.
Be sure to drop your letters or postcards in mail boxes inside the Vatican (yellow), not in Italian mail boxes outside the Vatican (red or blue).