There are no real counterparts of the Pokemon Association in the anime.
A possible counterpart could be the Pokemon Fan Club of each generation, but that isn't really found in the anime, but rather in the games. (As well as the manga)
It also should be noted that there is a Pokemon Association branch in the Sinnoh Region, but alas that is also found in the manga.
Hope I helped. :)
Source: Pokemonadventuresmanga.wikia.com/wiki/PokéFan_ClubPresident(Kanto)
pokemonadventuresmanga.wikia.com/wiki/Sinnoh_Director bulbapedia.bulbagarden.net/wiki/Pokémon_Association
