At this point in the game, I know of no color copiers that offer borderless printing. I spoke to a knowledgeable printshop owner about this awhile back. He told me that in the print industry they typically print things oversized and then cut of the edges.
Concerning Printers, you have a variety of solutions. Home printers typically use inkjet and that system is more easily adapted to borderless printing.
I believe wideformat printers have this option and it may also be possible with plotters.
Good luck on your search.