White Lithium grease (Lubriplate) is good for rubbing metal parts. If the old grease is sticky, you can clean it off with brake cleaner. Don’t let brake cleaner stay on plastic or painted parts for very long.
As mentioned, Lubriplate or similar is fine. Apply it very sparingly since you don't want grease to eventually spread to unwanted areas, causing further problems. Coins naturally deposit film and dirt onto coin mechanisms and that's why a small dab of lube is sufficient. Anything lubed or greased attracts dirt and grime causing friction... just the opposite of what you are trying to accomplish!