Most fruit can be classified as either climacteric or nonclimacteric. Climacteric fruit continue to ripen after they are harvested. Nonclimacteric fruit do not. Cherries are considered nonclimacteric even though other fruit in their genus like plums, peaches and apricots are climacteric. The two types of fruit go through very different processes when they ripen, which is why methods used to ripen climacteric fruit doesn't work on cherries.
For climacteric fruit, the ripening process is controlled by ethylene and carbon dioxide (CO2) production. Once the fruit reaches maturity, ethylene synthesis and respiration rate increase dramatically, which increases ethylene and CO2 levels in the fruit. They continue to produce these gases -- and ripen -- after they are harvested, which is why most climacteric fruit are harvested before they are ripe. Some fruit are sometimes considered ethylene-sensitive because exposure to ethylene speeds up the ripening process, but cherries are not one of them.
Cherries are nonclimacteric fruits because they don't ripen once they are picked from the tree. Unlike climacteric fruits, there is no spike in ethylene and CO2 levels in cherries as they ripen. They also do not ripen faster when exposed to ethylene the way climacteric fruit do. Because of this, the fruit must be ripe at the time it is picked. Most citrus and berries are nonclimacteric, as are grapes, watermelon and bell peppers.
Paper Bags and Ripening
The belief that you can help ripen cherries by placing them in a paper bag is a myth. Paper bags work by holding in the ethylene that fruit produces. The more ethylene, the faster the fruit will ripen. But this only works for climacteric fruit, which use ethylene to stimulate the ripening process. It won't work for nonclimacteric fruit like cherries. Ethylene causes cherries to soften, but not ripen.
Finding Ripe Cherries
The best way to tell if a cherry is ripe is to taste it. If tasting isn't an option, you should look for firm, but plump, cherries. Sour cherries will fall off the tree easily. Not all cherries are the same color when they are ripe, but dark varieties should become very dark before you pick.