Then it sounds like interferance as Jerry describes. You do have radio suppression spark plug wires and spark plugs, right? Does the noise go up and down with the volume or is it at a constant level? If it is at a constant level regardless of volume setting, I'd guess it's something in the radio and/or speakers themselves.
Otherwise I would take Jerry's suggestion and try playing the radio with the engine off and if the noise is still present, I would again think it is a problem with the radio and/or speakers. If the noise is present only with the engine running try Jerry's suggestion and also check your plugs and plug wires as radio suppression types.
I would think whoever rebuilt the radio for you would be willing to check it out again at N/C. If not, let me know who they are so I can not send my business there!
Let us know what you find out.