There isn't a way to obtain ribbons in-game in Black/White and their remakes.
However, the games themselves do have a ribbon system, which are mostly got through events and transfer from the Generation IV games.
>In Generation V, Ribbons are kept, and though they aren't obtainable anywhere in-game, they can still be seen in the summary screen if obtained in Generation IV or from an event, which are the only ways allowed to obtain Ribbons. Pokémon Black and White introduced a few new Ribbons, which are only obtainable from events, as well as a categorization scheme, separating them as League, Contest, Tower, Memorial, and Gift Ribbons.
Scrapped directly from here.
Hope I helped!