To keep them from swaying,first get plenty of foam pipe insulation. Get a couple of sizes one that will fit on the smallest tubes on the bike and some for the big tubes. Put each bike so that only tire to metal contact, or foam to metal, (or foam to foam on your nicely painted bikes) is contacting. Carefully pad them and tie them so they are pinned against the bumper and cannot move. It takes a while to get used to it but I do on my four bike rack all the time. I'm the only one of my friends who never scratches a bike on the rack. I don't scratch the car either. HOWEVER I rarely put my best bike on a rack, you still may may mark the paint with the foam or just a rope rubbing on the bike. Tie them [B]solid and padded[B]
My suggetion is use the bike with the most expendable paint job on the bike rack. ? If you have one.
You may be able to tie to the lower part of the bike rack or go under the bumper to something solid. If there is a lot of space between the bikes or the bikes and the car, a couple of the old "boat cushion" type life savers can hang on the rack and make good bumpers. So can boat bumpers.