All you need are two things: a piece of aluminium foil and some oil. Apply a light layer of oil to the light green flesh, cover your avocado with the foil, and store it in the fridge. Spray oil will make this easier, but you can also brush the oil on or use your fingertips.
The oil will act as a barrier to prevent oxygen from reaching the flesh of an avocado, which is the reason it turns brown. Your half an avocado will stay perfectly green for a couple of days.