Pokémon Rare event berries

[Reginald Fairfield]

There are some berries that have not been available very often. Custap, Enigma and Jaboca come to mind. I don't recall getting any of these since maybe X and Y with an event. Of course pokebank doesn't transfer items. Have I missed something that has come with these?

 

[Halloqueen]

The Enigma Berry found its way into X, Y, Omega Ruby and Alpha Sapphire through the distribution of Darkrai in 2016 as part of the 20th Anniversary celebration. Since you can acquire it, you can grow and use the Enigma Berry in Generation 6 but you can't send it up to Generation 7 and there hasn't been an event for Generation 7 where a Darkrai was holding the Enigma Berry.

I can't say anything about the Jaboca Berry or Custap Berry. I've looked around and it appears that neither has seen any form of release since the days of Generation 4 (other than one Japanese Mewtwo in 2013 for Generation 5 for the Custap Berry).