From the Super Mario Wiki
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Character Coins or Baby Coins are coins that the Yoshis can collect in Yoshi's Island DS. The Yoshi can collect a Baby Coin only with the baby on Yoshi's back that is seen on the coin. Collecting all eight Baby Coins in a world (or all seven in the case of world five) unlocks a minigame in the game's Hard Mode. The thirty-nine coins in the game are evenly distributed among Baby Mario, Baby Peach, and Baby DK.
Baby Mario Coins
Baby Peach Coins
Baby DK Coins