If you're got more peaches than you can enjoy quickly, eat a few and slow down the ripening process on the rest. In general, peaches are harvested before they are fully ripe, unless they are picked for immediate use. And, if the unripe peaches -- which are extremely firm when gently squeezed -- are left at room temperature, they will ripen quickly, often within a couple days. To keep the peaches from ripening too fast, store them in a cooler location.
Refrigerate the peaches in a drawer with humidity control. Set it on "high." The coldness slows down the ripening process and humidity prevents the peaches from drying out in the meantime.
Place the peaches in a brown paper bag and loosely close it if you do not have a humidity controlled drawer in your refrigerator. Set the bag in the fridge in the crisper drawer. The bag traps in humidity so the peaches will not shrivel up while they are ripening, and the coldness in the fridge will slow down the ripening process.
Store peaches no longer than two weeks in the fridge. They may fully ripen before this, depending on how ripe they were when they were first refrigerated.