There is no standard for the colours on the wires. I have seen completely different colours in different AT and PS/2 cables.
If you have the original cable, then you could repair it by soldering by colour and insulating using heat-shrink tubing.
Otherwise, you will have to follow the wire to the soldering pads on the circuit board and figure out which type of signal goes to which soldering pad. If you are lucky, this will be marked on the circuit board.
Otherwise, hopefully someone on this board has an identical keyboard and could test the wires on his board and help you with that.
If you are unlucky, then the only option is trial and error. With four wires, there are up to 4! = 24 different combinations to try.
However, you could make a calculated guess about which wire goes to "ground": it is often tapped in more places than any other signal line. On many circuit boards, the "ground" signal is also wider than all others. If you find "ground" then there are only 3! = 6 combinations left to test.
That is how I figured out how to connected my Dolch keyboard (it had a "RJ plug"): I got it right on the third attempt.
If you have to do this, then I suggest that you use an internal connector, so that you don't have to de/re/solder on each attempt.