Trap ball - Basically it is a Pokeball that you plant/rig in an area that Pokemon can be found. You leave it, then when you return after however many days, you find a Pokemon in it. The longer you wait, the better the chance of it being a shiny/rare Pokemon.
The last sentence is what I'm iffy about. As this is a fic rather than a game which doesn't necessarily have the greatest steps in logic, then people might wonder why is it that the trap ball gives you a better chance at getting a wild Pokemon just for leaving it there longer. After all, once something gets in there, shouldn't it stay there? What exactly about the length of time waited corresponds to rare Pokemon being caught as opposed to more common ones?
Dual ball - A type of Pokeball that would carry a second Pokemon in it, when you throw it, the ball randomly chooses which of the two Pokemon to send out. This would give you the opportunity to have up to 12 Pokemon with you. It would also add depth to a Pokemon battle, having to come up with strategies for more than one situation.
It's...kinda interesting, although you'd have to consider firstly why this ball is made, why the limit of 6 Pokemon is suddenly doubled (because that's the limit rather than the number of Pokeballs you carry) and I do wonder if that runs the risk of arguably being risky considering it's storing two different Pokemon in it. Might be a fun concept to play around with, but it could use considerations.
"X" ball - The villains of this region developed this ball. It has the ability to catch trainer's Pokemon. If this were a video game, the main character would gain access to it right before battling the leader of the group, who would have, essentially, legendaries, that you would have to decide which of the Pokemon you wish to capture. It has 100% catch rate. There is only one (like the Master ball).
Sounds like a Snag ball (ala Colosseum and XD), only just a one-off Master ball... but if the villains have it then a) why did they only make one, b) why didn't they use it already, and c) how did the character gain it? (More questions to consider for your story's plot, but hey!)