PokéBase - Pokémon Q&A
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It doesn't happen in any generation apart from Gen II, and there's no definite time frame. It just says "over time", the Berry Juice will harden into a Rare Candy if held by a Shuckle.

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There has to be some formula or set value or range of values for this. Points to whoever can figure it out!
Actually, someone already did: http://asia.gamespot.com/pokemon-black-version/forum/c-d-shuckle-should-have-its-berry-to-berry-juice-to-rare-candy-ability-returned-61941787/

Different berries take different amounts of time, apparently. I didn't link it because it's a forum post (reliability), and not a site post like Bulba or Serebii.
Last time I checked, Sitrus Berry wasn't in Gen II. :P
That's a theoretical "What Gamefreak could do with reintroducing this with the new berries" not any actual numbers.
I need to read things more carefully. :P