Does "non acquistabile" mean that tickets are unavailable for online purchase; or does it mean that the train is not available for the desired timetable?
We plan to purchase 2nd Class tickets at the station on a regional train, and will be traveling on a Sunday.
Not available for on line purchase. There is no advantage to purchasing in advance other than a day or two when you are there.
Most Regionale (R) train runs on the Trenitalia website cannot be purchased online. You will see some but most will have NO in the BUY column. The R trains are not like the Eurostars. No reservations or seat assignments are possible. It's like a local bus. You buy your tickets, get on and then find your seat. If none are available, you stand. Buying tickets at the train station is just fine. Note that there are usually fewer runs on Sunday.
It could mean that tickets are not available on-line, but it probably means that you are looking too far in advance or that the train has already left the station - when you go to trenitalia.it the day and hour fields default to your current location, so in my case California is 9 hours behind Italy so trenitalia will show the schedule for trains that left 9 hours ago if you don't reset the fields to Italy time.
By the way if you're traveling on a Sunday be aware that many trains don't run on sunday. Each station has a printed schedule board and if a listing says "non circola nei giorni festivi" it means the train doesn't run on sundays and holidays. Just to be confusing, "circola nei giorni festivi" (with the word "non" left out) means it only runs on sundays and holidays. Also be aware that the ticket window at many stations is not open on sundays and that they keep banker's hours on days that they are open, so you may need to use the automated ticketing machines. The big stations have modern machines, but the smaller ones may still have a clunkier device. You need to know the 3-digit code of your destination. There is a sign next to the machine with the codes. You can't feed money into the machine until you press a button that indicates you accept the price. Many machines run out of change and will dispense a change voucher instead which you can redeem at an open ticket window up to 60 days later. Finally don't forget to validate your ticket before you get on the train. There are yellow ticket punching machines (convalidare) at every station. You probably can't/don't have to do this for web tickets, but you must do it for ones you buy at the station or at Tabacchi shops.
