It's probably as challenging to find a used Vatican City stamp as it is to find a non-Catholic living there. I do have a few, but for the last year-and-a-half I've been fortunate to exchange with Michele Castino of Milan. My Vatican City is now something to see. Holy See, See of Rome, Petrine See or Apostolic See.
Thanks to Michele's generosity, my mainly-mint collection has burgeoned into its own album. I took a quick video of the results: new cover, glossary of some Latin/Italian inscriptions, the collection, then my collection of Pope John Paul II.
Youtube link here.