The green spots found on some copper coins are called verdigris this is a copper salt like rust. It is usually copper acetate, but can be a copper hydroxide. Neither of these would come off with any kind of oil. The copper salts will flake off with just rubbing - and that is likely why some people think olive oil, or cooking oil will remove it. In fact it's just the mechanical friction of rubbing that causes it to come off. I have heard that the juice of a peach will remove it but I have never tried it.
Some forms are soluble in water so it might be possible to use hot water and rub them with your thumb or very lightly with a toothbrush to remove some of the material. If that does not work the only other option is an acid dip. Chances are the coins are pitted from the corrosion and removing the verdigris will expose the pits and they may look worse after dipping than before. You will more likely scratch or damage the coin unless you are very careful while doing this.
The acid dip can be made easily from salt and ammonia mixed together. If you do this be very careful and use gloves. Dip the coin for a short period then rinse and wipe clean.
I wouldn’t undertake this job lightly. You could first try it on inexpensive coins until you have got it right and then progress to the more expensive ones. My recommendation is if you can put up with it the way it is then that is the best option.
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