|Subject: Buying Italian Train Tickets in Advance|
While it has been discussed that buying said tickets on the Trenitalia website is only for Italian residents, it is possible to buy tickets in advance through travel agencies in Italy.
Perhaps a friend in Italy, or one of your hotels could give you the name and number of a reputable agency that you can use.
If you are in the USA, perhaps the Italian National Tourist Office could give you a recommendation. Or one of the large Italy touring companies, a local TA, etc.
Buona Fortuna, Debbie in Pittsburgh