I guess I should only include fresh fruits, because a lot of fruits last for a long time if dried.
Navel oranges seem to last a long time, as do apples. Pomegranates are also relatively long lasting, though not quite as long. Tamarind and carob are sort of dried fruit so I don't know whether to count them, but they also last a reasonable amount of time. Pineapple guavas are also relatively long lasting before they ripen. Fuyu-type persimmons are also relatively long lasting as long as they aren't bruised.