In the 16th century, being "on the money" meant an arrow or a dart being on (or near) a specific physical coin (i.e. the money), like in a tossing or shooting bar-bet.
Being on merely a money (or some money) would likely not be as impressive in said circumstances, and so whilst being grammatically possible in English, it shouldn't seem so likely the sort of thing anyone would ever have had to say.
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In the 16th century, being "on the money" meant an arrow or a dart being on (or near) a specific physical coin (i.e. the money), like in a tossing or shooting bar-bet.
Being on merely a money (or some money) would likely not be as impressive in said circumstances, and so whilst being grammatically possible in English, it shouldn't seem so likely the sort of thing anyone would ever have had to say.