According to the Online Etymological Dictionary the origin of the word is:
1580s, originally in slang phrase to make a coax of, from earlier noun coax, cox, cokes "a fool, ninny, simpleton" (1560s); modern spelling is 1706. Origin obscure, perhaps related to cock.
But how did a noun meaning "fool" end up as a verb meaning "to influence?"
Is it just because someone who is influenced easily is a fool?