Bananas turn black in the refrigerator mainly because of the chemical reactions in their peel.
A non-ripe green banana peel contains a plant hormone called ethylene. This gaseous chemical is responsible for helping ripen the banana to yellow color. At the same time, some natural acids are also being produced which regulate the ripening process and make the banana sweet (inside the banana, the large number of enzymes of Kreb’s cycle convert citric acid, mallic acid and oxalic acid into glucose, which turn the banana sweet during the process of ripening).
When someone puts a banana in the fridge, the production of these natural acids slows down as consequence of the cold temperature and, as a result, the ripening process of its interior slows down.
However, in cold temperatures, the physical state of cell membranes in the banana peel changes causing leakage of the enzyme polyphenoloxidase which oxidize phenolic compounds that leak from the vacuoles of the cells ( this enzyme polymerises them into polyphenols similar in structure to the melanin formed in suntanned human skin), and hence producing the dark colour.
Nonetheless, bananas can be stored in the refrigerator for few days. Despite the peel of banana becoming dark, its content will remain firm and delicious. Coating the banana with organic wax to prevent contact with the oxygen of the air can also slow down the blackening of the skin.
Another solution is to peel the bananas beforehand, put them in a sealed freezer bag and then storing them in the fridge. Coating them with little bit of fresh lemon juice can help to reduce its darkening process even more.