Along the lines Pamela suggested they would work really well to place around the inside edge of a wire dog crate. Just make the bottom pad in a co-ordinating fabric. Foam for stuffing the bottom pad is available here on ebay pretty inexpensively. Put upholstery foam in the search and use one 2-3 inches thick.
Hi. I normally just lurk, but had an idea pop into my head, lol.
If you sew at all, you might consider cutting this up into strips. If it's a 4 pc bumper set, just cut the long sides in half. Resew the cut ends, and then sew the strips together to form a padded play/nap/floor mat for your little one to lay on.
If it's the long, one piece type of bumper, you'd have to do a bit of measuring to try and get, say, 6 pieces of equal length. Most bumpers are at least 8 inches high, so that would give you a mat that's 4 ft long. Plenty long enough for a 2 year old.
Here's something that you could make your daughter:
Just tie the ends together, and it's virtually no sew.