How do I cater for high instantaneous current in a power supply?
It does. Peak loading like you describe can be dealt with in one of two ways - rate the power supply for the worst-case load continuously, or temporarily. Either way, the power train needs to be able to deliver that power.

Since the worst-case load is only 2A, it is a reasonable design point to make the power supply work at 2A continuous output - then you'll never have an issue.

If you're talking about a 100A power supply that needs to deliver 200A temporarily, rating the power supply for 200A continuous is most likely overkill. In this case you can put a timer on the overload protection to allow the overload to persist for the short interval that's needed. The power train components in this case have to be rated for the surge, not the higher sustained steady-state - often the 100A power train parts could handle 200A for a few milliseconds as long as the thermals are managed well.