From PinataIsland.info, the Viva Piñata wiki
You can use the Bouncer Board to ban pinatas from entering the garden. You must be a Master Romancer of the pinata species before you can ban it. This is very helpful if you want a special pinata and pinatas you don't want keep showing up.
Each species you have Master Romanced can be banned or unbanned individually by opening the Bouncer Board and selecting the pinata from the list. Note that arctic, desert, or evolved species, such as Reddhotts or Red Flutterscotches, will not appear on the bouncer board (since they don't visit your garden from the wild).
Banning a species does not affect any pinatas of that species already in your garden.
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