Supposedly the biggest cost associated with refurbishing a car is passing the Amtrak inspection of the bogies, axles, and wheels -- I believe they have to be completely replaced at 40 years of age. When a railroad retires a car, this equipment may be close to end-of-life.
Many freight railroads still have "office-car specials" -- passenger equipment for the executives to use. Those would probably be the easiest to get up to Amtrak specs.
Trivia: Amtrak will only run trains with private railcars at a maximum speed of 110 mph. On the Northeast Corridor, private railcars are only allowed to be added to the overnight Northeast Regional train which normally travels at 125 mph -- but there's enough padding in the schedule that they can slow it down to 110 without affecting the timetable.