Define privately operated. There are a lot of shades of grey.
In the "true long distance" category, the Rock, SOU, and DRGW held out, with DRGW last in 1981. You also had some quasi-long distance trains operated as bigass commuter trains like the Reading train to Bethlehem. Chessie operated South Shore with no subsidy until 1977, and a private shortline operator ran South Shore until 1989 under private ownership but subsidized. Same thing happens when BNSF or UP operate for Metra, but they don't own equipment anymore. You've also got the Texas-Mexican train that ran on the border for a few years around 1989, private equipment and no subsidy. Also, what about Brightline?
By one definition or another, we have had private passenger trains through the current time. It's an interesting thought exercise.
The new Acela: It's not Aveliable.