After getting the Mystic Melody, go to the City Escape level. Play the third mission, but do not get the Chao until you have 999 rings and 99 lives. This is useful when you need rings to buy very expensive items. If you just need a certain amount of coins, keep playing this stage until you get that amount.

As Sonic, go past the first point marker. You must have between 60 and 80 rings to get the first extra rings. At the first turn, hit the boost pads, flair flip, and grab the magnetic shield, Then, flair flip up the ramp to get an extra 30 rings. Keep the magnetic shield on until you get to the Gun truck that chases you. Go down in this order: right, then turn left, and run down the path. Get the coins, then turn right at the first turn to get some rings. On the next turn, turn right to get a lot of rings then go left to get all the rings.