Infinite rings for Black Market purchases! There are three methods to get rings in SA2B.
Play a level over and over to get rings. Sonic and Shadow are best for this because their levels go the fastest. City Escape or Radical Highway both have decent amounts of rings in them and they're very easy to do.
Using Knuckles or Rouge, start a level and then just start digging everywhere in the ground. You'll find random power-ups like shields and sneakers, and you'll also get ring boxes with anything from 5 to 20 rings in them. Don't dig in exactly the same area twice in a row.
If you're really patient you can get 999 rings on any level this way, but it does take ages.
This is by far the easiest way to get rings, although it's definitely not legit. Go into Chao World and get an item from Black Market - the more expensive the better. Put the item into a garden, then leave Chao World and save. Turn the Gamecube off at the power switch.
Turn it on again and go back into Chao World. Sell the item you bought.
Now reset the Gamecube (reset button). Go into Chao World again and you'll find your ring total was updated and the item is still there. Keep selling the item, resetting the Gamecube each time, for as many rings as you want.
When you're done, complete a level in the game to save your new ring total permanently. This is important. If you just turn the Gamecube off without doing a level, the game will forget.
Shiny Chao eggshells and the wool hats are worth the most.