I was booking roundtrip Rome to Naples for June 18. Due to the size of my party I have to do 2 transactions. The seat numbers weren't showing correctly and I realized it isn't allowing me to book a return on the 18th. Even when I try to do a one way ticket and enter the date of the 18th, when I'm choosing my seat number the date has changed to the 19th.

Anyone have any suggestions on what I can do? And of course I have economy seats with no refunds.

Phone them.

have your credit card company block the payment?

Are you saying the first transaction went through correctly and the second set of tickets isn't?

You didn't list the exact trains you were trying to book, but the ones I selected allowed me to select seats (I was attempting 5 tickets), but it said enough seats is not available on the r/t. That may just be for that particular price.

When using the trenitalia site, you have to put in the time of travel as well as the date. If you allow it to default to the time on your computer, and if the time is late in the day, the schedules will roll over to the following day. The trains on the following day will have an asterisk referring to a note that points out this fact, but many, many people miss this and end up in your situation. Even though the tickets are nonrefundable, in the past Trenitalia has been know to change them if you call or email them explaining that you had asked for tickets on the 18th and just noticed that the date is the 19th. I can't guarantee that they'll change them for you, because it clearly is not possible according to their terms of sale, but it's worth a try.

Your problem with booking a return on the same day is probably also related to this fact. Try entering 1 AM as your time of travel, to make sure that all the trains shown are on the same day.