Convert my RGB file to CMYK without any changes in its color tone

I have a photoshop file design in RGB which I want to paste to a photoshop CMYK file which will be printed on a bill board. But when I paste content of RGB file to CMYK file its color tone changes heavily and it becomes very dull.
If anyone has solution of my problem (convert my RGB file to CMYK without any changes in its color tone) I will be grateful to him