Coining in cooking means to slice a vegetable through the diameter into small, thin pieces about the size of coins. Usually the vegetables that you’re asked to “coin” are stalk vegetables. You wouldn’t get very far in applying coining to a tomato.
Usually a recipe will tell you how wide the pieces should be, or the size will dictated by what you are slicing. For instance a stalk of celery or a broccoli stalk is going to be as wide as it comes, and that’s all there is to it.
If the size of the slices is not specified, presume it to be about the size of an American quarter or a British 10p coin.