Consistent Color Issues

Most of the time I don't need accurate colors, but occasionally I'll get a job that I have to send to get printed, like a banner and that's where my issues come in. It seems like no matter what I do the colors of my designs get totally washed out in the saving process. If only I could print RGB....

This is How I designed it:

 PNG

This is how it saves:

 CMYK JPEG

I designed it in CMYK so idk why it limits the colors further after saving.

I use the  U.S. Web Coated (SWOP) v2 Color Profile

I do have issues of Corel just changing my color profiles at random, but I don't think that's the issue here.

And TIFF Files seem to give a similar if not worse result as JPEGS.

Please help!