If you look at PokemonMinigameTriad, you can search up that you can buy cards that you own in your PokéDex, I don't think it would be hard adding an item with a descrition of what it does, stick that in your key items pocket, or, I would probably make a new pocket, and use a script directly after the adding of the card:
Which quickly browsing keep be any of the following;
TriadCard.new
$PokemonGlobal.triads.pbStoreItem(item,quantity)
The only thing I can see being a problem, Triad, registers cards in your PokéDex, so if you try to recieve a card that isn't in your Dex, I can't say what would happen... It's also possible that there is no way to do this, but as I said, I only had a quick scout and that's what looks to be the more achievable option... I can't offer you a solution but maybe this is a good place to start looking into, believe me, without actually playing aruond with the scripts you won't learn anything, I'm learning but Maruno still finds flaws in my methods, have a look in the Triad script section and see what you can come up with, then message back.