This is pretty simple in practice.
1) At the start of acts 1-2 of Green Hill, Marble Zone and Spring Yard. Perform a save.
2) Collect 50 rings; save as needed for sections you are likely to take damage.
3) Get to the end of the act, again saving to insure you keep your rings.
4) Jump into the giant ring at the end of the act and save again.
5) Now keep trying to grab the emerald, reloading the save if you fail.
Theoretically, you have until Scrap Brain Zone act 2 to aquire all emeralds, though it is much more difficult to keep your rings.