if you don't want cotton perhaps choose a poly blend? not sure why you don't want cotton- all of the table clothes i've made have been cotton-
you can purchase vinyl from stores like joannes= they also carry many different home-dec fabrics in various widths- perhaps one of them would suit your purpose. the joannes in our area have a very large selection of home-dec fabrics---including table cloth fabrics from linens, to plastics.