If you don't want to use the unripened avocado right away, according to this site
Store Cut Unripe Avocados - If you have cut open your... avocado and found it to be unripe, sprinkle the exposed flesh of the avocado with lemon or lime juice, place the two halves back together and cover tightly with clear plastic wrap before placing in the refrigerator. Check the avocado periodically to see if it has softened up enough to eat. Depending on firmness when the fruit was cut and temperature conditions, the ripening process will vary
Another user suggests to use vitamin C powder instead, as her experiments show the vinegar would darken the avocado.
Ironically enough, there's a solution to ripen the avocado (almost) instantly if you want to use it right away. This link talks about "instantly" ripening a foil wrapped avocado by baking it in an oven preheated to 95°C/200°F oven. Cooking time can start as low as 10 minutes. Keep checking every 10 minutes until it's soft enough for your use. After it's been in the oven, let cool and unwrap.
Note: that the taste and texture would be changed after thus heating the avocado, but it should be usable right away after baking.
There's also uses for the unripened avocado seen here