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 likelyhood of the child also being a wildcard. To know if your piñata is a wildcard look at it's value. A wildcard piñata will have a value of 10,000 or more coins higher than it's regular value.
How to get a wildcard
To get a wildcard you need to follow all the romance requeriments 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 wil 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 the game Leafos said that the chances to you get a wildcard is a million to one, but this information is false.
Leafos said in special occasions will have a chance to a wildcard piñata born