I assume this is a K4600 series monitor that has 2 plug in boards. One is called the Video IO board and is the one with the inputs for the signal and stuff, and the other one is the X-Y deflection board that has more components and some variable capacitors to adjust horizontal hold among other things.
Ken Layton posted a summary of each board model # (e.g. 313, 316, ...) and which rev of the 46xx they came with, however I believe any of them are swappable with any other board.
You could also simply replace the single pot that was broken, however it likely will cost as much as another used board.