I made a little cell phone case once but I now use it for my driver's license, credit cards, money that I carry in my pocket instead of taking a purse. It is small (my cell phone is one of the "old" really small ones) but I think it would work for an MP3 player. You could also use the back pocket from an old pair of blue jeans & attach a strap. I think your grands would like it made from jeans. If you google "cell phone" case tutorials you may find something you like. Mine was really easy to make. PM me if you want me to scan the instructions & email them to you. Mine doesn't have a strap but it would be easy to add one. Mine has a flap that folds over & is secured with velcro.
Here's a tutorial similar to the one I made (you could adjust the size for the players):
https://makeit-loveit.com/arm-band-pouch