hi! if you don't get an in-depth response here, you might try x-posting to the sub specializing in word origins, /r/etymology. Meanwhile, to get you started, the Online Etymology Dictionary says this for the verb to coin:

coin (v.) "to coin money," mid-14c., from coin (n.). Related: Coined; coining. To coin a phrase is late 16c. A Middle English word for minter was coin-smiter.