copper-nickel is extremely difficult to clean. Much depends on the dirt. If it is mud, dissolving it with water and drying well will help. If it is fatty, soap will work wonders. If it is oxydation, look for another coin. You will not be able to remove it without damaging the coin. If it is something else, try remove it with your nails.
Copper oxydation can be removed safely. My favourite method is soaking it in olive oil and attacking the oxydation with a wooden tooth pick every two weeks or so. This can take months, but it is perfectly safe.
In principle, use chemical cleaners only when you know exactly what you are doing. Many chemicals will damage the coin. One extremely bad example is
Cilit Bang, which can ruin any coin. It will spectacularly turn the "nordic gold" used in euro coins into a horrid pink.
Coins turned black may be because of treatment with the wrong chemical, handling with people who also handle acids (fish mongers and vegetable sellers!), but there are many other possibilities, like chemical treatment at the mint, lacquer (used by coin collectors 100 years ago) and heat.
When treated with water or water and soap, only copper and bronze coins change colour, (provided the coin is dried well.) Discoloured coins can be repaired by keeping them in polluted air for a long time, e.g. in a window looking out on a street.