A few ideas on how to solve CE test failures…

PSU Noise?

Try powering the circuit from a battery without the PSU and re-test? This can confirm if PSU is the source of noise.

Use a DC power line filter, e.g. Murata BNX016-01 etc

If PSU is conducting test noise through it

Are low voltage cables sitting over / near the PSU and coupling noise? Is there a cover option for your PSU that might prevent this and is worth trying?

Applying a ferrite around the mains cable or around the live and neutral cables individually can solve this conducted issues.

Use a mains filter can also solve this conducted issues. Note that often selecting a lower amp rating of filter will give you better filtering performance (higher inductance) so don’t just overrate without considering this. If you’re not using the full power of your PSU can you lower the mains input fuse rating and use a lower current rated filter?

Voltage spikes make it through to outputs

Add tranzorb diodes to inputs and outputs to clamp them and stop them arriving and being passed out. Applying to PSU low voltage outputs can be good too if spikes can get in through the mains connection and be passed through the device to the outputs. E.g. a 50V 1.5KE can be hand soldered on easily.