Fruits that fall into this category include avocados, unripe bananas, nectarines and peaches, pears, plums and tomatoes. Don't store ripe bananas in the frig. Some fruits and vegetables emit a gas that can make produce ripen faster Apples; Avocado; Ripe bananas: If you want to slow the ripening. Wondering how to store and ripen your favorite fruit? These tips tell you what to do with everything from apples to avocados, pomelos to.