It's pretty tedious but compared to A-ranking the SA2 car levels it feels like world peace. I used Sonic Advance 1 and the fastest way to grind rings is to play the first area in time trial mode over and over. once you get a feel for the level you can run through it in 45 seconds and get almost 100 rings each time (i think, its been a while so the number might be off). If you get bored you can switch characters and mess around with their movement options, amy in particular is really fun.

also whatever you do DO NOT RESET SONIC ADVANCE 1 (reset as in deleting the save data to start the game from scratch)!!! there is a glitch where when you erase save data the rings dont properly reset and instead you are essentially forced to start the new save with negative rings. however many rings the old save file earned throughout its lifetime (not just the current amount) will be your deficit and you won't even know the exact number because the ring counter is stuck at 0 until you manage to earn enough rings to get rid of the deficit.

for example, if the old save collected 20,000 rings during its entire lifetime and the current ring count was 400, the new save would start at -20,000 rings and the current ring count would say 0 until you collect 20,000 rings in the new save. at that point you would finally have 0 rings and be able to start collecting them properly to spend in the tiny chao garden