If you don't already know, be sure you have an odd number of ribs or the weaving won't work out right and control the tension of your weavers. The different thicknesses and shapes will take different amounts of tension. This is something you will have to play with. By the time you get to the end, you will have it figured out.
You can use natural materials for these quivers. Cane, blackberry canes or small shoots for the ribs(these will have to be split) and honeysuckle, grape vines, outer and inner bark of trees for the weavers.