Super simple way to make a ring holder...all you need are straws, felt, glue, and if you want it covered with a nicer fabric, that.
1. Wrap straws with a sheet of felt to desired circumference. Glue in place.
2. Cut felt/straws to dimension of box that you want to hold rings.
3. Stuff them in the box. If you want, take your fancy fabric and tuck it in all the places between the felt/straws, then tuck in each side of the box.