For this little project, I re-used a small gatorade bottle cap. In my opinion it's the perfect size for a pincushion ring. The regular size gatorade bottle cap is probably perfect for a pincushion bracelet.
I referenced the tutorials below, they were super helpful. One thing I did different though, was use a leather hole punch to make the holes in the cap for the elastic. As long as the plastic isn't too thick it should do it, it did the gatorade cap.
Basically all you do is take a thin elastic and run it through the holes. Make it loop and your size then knot the ends in place. I made my fabric circle 4 inches in diameter (using some leftover cotton from this
previous refashion of mine). Gathered it, stuffed it and hot glued it into place. Lastly, I took a 3/4 inch cotton lace trim and wrapped it around the lid edge for embellishment.