Electronic transformers for the low voltage lighting, I assume? Mixed circuit for lighting and power in the kitchen? Try leaving the radio where it is, run an extension cord to another circuit and see if the noise goes away. If the noise goes away, the power outlet may have to be moved to another circuit. Otherwise move the radio as odds on its the transformers producing the noise.
A small AC cap in parallel with the incoming supply to the radio might provide the needed RF attenuation.
Better still would be to place a standard "CLC" filter inline with the incoming supply cord to your puck lights..... sounds like you have one of those cheap and nasty Chinese switching PSUs. Many are missing the RF filter they need to pass FCC certification! They are notorious for sending a proper unit for certification and then doing the old switcheroo when it comes time to put them on the boat. In this case, all you would be doing is adding a little box that had a line choke and a AC filter cap (0.1uF is enough) on each side of the cap in this case. Place the filter box as close to the main PSU as you can get it.
The Radio Shack ABS plastic project boxes make good, safe enclosures for this sort of thing.
Mouser Electronics sells some EMI/RFI filters with terminals, all you would need to do in that case is solder your wires to it and place it in an enclosure. This route is the easiest and will probably provide the best performance.