Apparently the first ever useage of the phrase "to coin a phrase" was by a George Puttenham in his English Poesie in 1589.
"Young schollers not halfe well studied... seeme to coigne fine wordes out of the Latin."
The verb to coin appeared in 1330 and means "to create money by stamping metal". It seems that the verb was used by Puttenham to mean creating new words too.
The meaning to create a new turn of phrase was adopted commonly in the 1940s and seems to be an evolution of Puttenham's useage.