This is the ring display I just made. Very easy and cheap to do, and took about 1½ hours.
The frame is 5 x 7 with a stand on the back, one I already had. If you don't have one, check the thrift shops or dollar stores before spending more than a couple of dollars.
First remove the glass and any pictures and replace the backing.
I read about one where they used rolled up felt which would have been faster and easier but I didn't want to spend any money so this is how I did it.
I had some polyester velveteen but any fabric that doesn't fray would work. I tried just rolling it up but unlike felt, my fabric needed some help. I used a piece of old rope cut to fit just short of the opening in the frame to form a core for the roll.
I cut the fabric wider than needed to make the trimming easier afterward.
I whip stitched the rope to the edge of the fabric, beginning and ending short of the rope ends. You could use white glue or hot glue for a faster way to do it. Then just start rolling the fabric up as tight as you can, keeping the ends even and not telescoping. Once you have the thickness you want, trim off the length excess. Then unroll it so you can use it as a template for the rest. I didn't know how many I would need so I just cut 6 until I saw I needed more and then cut more.
Now make your roll again and either glue or sew the edge so it does not unroll. Only sew or glue from one end of the rope to the other, not beyond. You don't want to cut your thread and cutting through glue is hard.
Lay your frame down, front side up like a tray. Cut one edge of your roll close to the rope and lay it in the frame to see where it needs to be trimmed off. Cut that end to size. Keep making rolls until you have enough to fill the frame. I also used a marker to color the white ends of the rope so they would not be seen.
In my case 10 rolls were not quite enough so I added another. That worked nicely as once they were squished together it gave me a tight enough fit to hold the rings.
Now you can glue the rolls in place, seam side down. I used a white glue as it gave me time to arrange the rolls evenly. I just ran a bead of glue down the seam of the roll before placing it on the frame backing.
Give it time to dry and there you are!
This would easily work with a frame to hang on the wall. Mine is made to display rings I am taking to a craft show but it makes a nice display to set on a dresser too!