Conditioning input power supply on PCB
There are lots of possibilities, and it really depends on how much energy you expect to come down that cable, which in turn depends on what is in your environment, and also maybe what is driving it. (If the mains supply is just an unregulated transformer + bridge + reservoir cap there could be spikes coming from the mains itself).

One possibility is a transzorb which can simply clamp spikes coming down the line - it's basically like a fast zener (zeners have too soft a curve and are usually too slow for this kind of function).

But the problem is knowing how much energy is in those spikes and how to absorb it. A small amount of series resistance along with some C/L filtering can also reduce the amount of energy hitting your circuit and damp the ringing. (there are various commercially available filter modules as well.)

Is the issue happening when the circuit is plugged? or are you hot plugging the cable and getting spikes as a result of that?

Without knowing more specifics like the amount of DC current you draw and having some rough idea of the source energy it is not really possible to be more specific. This is EMC design, and there tends to be a fair amount of trial and error in getting it right. But this can give you a start point.