A wild-card is a rare piñata with additional or modified parts. To get a wild-card you need patience. If the parents of a piñata are wildcards there is a high likelihood of the child also being a wildcard. To know if your piñata is a wildcard look at its value. A wildcard piñata will have a value of 10,000 or more coins higher than its regular value in the original Viva Piñata game, or ten times its original value in Viva Piñata: Trouble in Paradise.
How to get a Wildcard
To get a wildcard in the original game you need to follow all the romance requirements of the breed of piñata you want and keep breeding them until you see the normal romance heart flashing.
When the heart of the piñatas are flashing, it is a signal that you will get a wildcard piñata. When start the romancing mini-game you will see some hearts. Collect all the hearts before going to your partner. If you collected all the hearts in the mini-game you will get a wildcard.
In Viva Piñata: Trouble in Paradise it is much easier to get a wildcard piñata. You need to get seven or more Piñatas of the kind you want to have a wildcard of, then romance them. Collect all of the hearts quickly in the mini-game. If you collect the hearts and then reach the partner quickly a "Wildcard Bonus" will be listed on the bonuses (and possibly "Twin Bonus" as well), which will mean you will get a Wildcard piñata.
In the game Leafos said that the chances to you get a wildcard is a million to one, but this information is false as you actually have a much higher chance of getting one, at arround 10000 to one.
Leafos said in special occasions will have a chance to a wildcard piñata born.