If you have crown moulding then you could hang ribbons or string from that and affix the quilts to those.
I have covered foam core board with fabric before, and that was light enough for even a dodgy adhesive to hold it up.
Depending on the size though I might go for a three-paneled room divider. It would be free-standing, tall, and you wouldn't have to damage the plaster on the walls. (I've lived with plaster. If I ever have to do it again I'm going to go to a trade school or something to learn how to fix it after I do stuff to it.)