It's probably between 12 and 72 hours for the "berry cycle " because in X and Y, the berries from the berry tree fall every 48 hours, so come back to the same berry tree every once in a while, and a good way to get berries in R/S/E is to look for all of the berry trees, and while your looking, the others that you have picked the berries from will start to grow back. It's genius!!
Hope I helped!