That the problem is the wrong wire is attached to the DARK screw on one or both switches........
BUT trial and error works safely here.......all the wires are "hots" that are normally switched......50/50 chance at each switch........
AND put yourself in the "shoes" of the first electrician.....the common wire/dark screw is the "special" wire in this bunch...........Didn't you say there were two blacks and a RED?.....try that as a common "first"........the other "travelers" can connect to either brass screw(s)..........