This is very easy to do.

First go to the Chao Black market.
Buy the most expensive item. (in my case it was the watermelon)



Bring the item to one of your gardens and then exit the Chao world to save the game.

Re-enter the Chao garden, get your item and sell it to the Black market.


Then go to the options menu and change something. (You can just select rumble on twice)


Then exit the options menu to save and Close your game.

(Do not press Exit Game from the pause menu. Since that will save you selling your item)
I put the game in windowed mode, so I can just click the X to close the game.



When you Re-launch the game and go to the Chao garden, your item (in this case my watermelon) will be there, but you will still have the rings from when you sold it.


Going to the options menu and saving will save the rings you have, but it won't save any changes to the Chao world.

With this trick, you can get as many rings as you want.