From the Super Mario Wiki
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They can be forced open by any attack and reveal their contents upon doing so. As their wooden appearance compared to their metal counterparts indicates, rather than containing a treasure, wooden chests contain more common items like garlic, a Smiley Bomb, or coins. When Wario re-enters a wooden or a steel trapdoor after having completed the sub-level inside, he finds a wooden chest with coins in it where the red diamond used to be.