The Groundhog Stone. Just by looking at it, you would have no idea it had replaced the original. The only give away was the subtlest of noises, a ticking sound every second like that of a clock that one could only hear if they held it up close to their ear, and even then ever so faintly.
This stone would grant up to three wishes a day, regardless of whether the stone was in one person's possession or switched. After three wishes, the light it gave off would grow a bit fainter. However, its unique power was in what happened when the clock struck midnight.
At midnight, the user would immediately fall asleep (if they weren't already), and the day would be reset. Yes, kind of like that movie the title is referencing. Any wishes made before then would be retained, with reality adjusting to match. So if Jon wished to be 6 feet tall on Monday evening, he'd wake up the next day on Monday again, already 6 feet tall. Most importantly, after waking up, the user (and the rest of the world) would be unaware of the wishes and would think their life had always been that way.
The only way to stop the day from resetting was to not make any wishes. If even one wish was granted, the day would repeat.