There are wireless systems, but the reports I've seen on them indicate they are problematic in longer vehicles, e.g. motorhomes. And running a new cable under the coach is no big deal, though getting it up to where you want to mount the camera may take some creativity. And you probably will need a new cable, both to to give a quality color signal and to match the connectors on camera and monitor.
I'd suggest a better quality bran, even though they get pricey. There is a big difference in camera performance with increasing price. The cheap ones don't handle a broad range of lighting conditions very well (and back-up camera gets everything from direct sun in the lens to shadows or morning and evening lighting) and typically have a rather narrow field of view. I have a color Sony that auto-adjusts for lighting and gives 170 degree field as well as a long way down the road behind me. I can even see the ladder on the back of the coach!
Here's one system by Audiovox
http://www.pplmotorhomes.com/parts/rv-mirrors/color-backup-camera.htm
And a source for Sony
http://www.rvcams.com/merchant2/merchant.mvc?Screen=CTGY&Store_Code=RBCARVS&Category_Code=15&gclid=CKfu0pDl36YCFVZc2godbD5o6Q
And some other brands
http://www.rvcams.com/merchant2/merchant.mvc?Screen=CTGY&Store_Code=RBCARVS&Category_Code=11
