Coax
late 16th century: from obsolete cokes ‘simpleton’, of unknown origin. The original sense was ‘fondle’, hence ‘persuade by caresses or flattery’, the underlying sense being ‘make a simpleton of’.
wiktionary
originally (1586) in the slang phrase to make a coax of, from earlier noun coax, cox, cokes "fool, simpleton", itself of obscure origin, perhaps related to cock(“male bird, pert boy”). The modern spelling is from 1706.
Shortened from coaxial
etymonline
coax (v.)
1660s, "lure with flattery and fondling," also in early use "treat endearingly" (1580s); "make a fool of, impose upon" (1670s), probably derived from slang phrases such as make a coax of, from noun coax, cox, cokes "a fool, ninny, simpleton" (1560s), which is of obscure origin, perhaps related to cock (n.1) in some sense. OED speculates that the verb was in vulgar use long before it appeared in writing, thus the order of appearance of the senses is not that of the sense development. Meaning "to manage or guide carefully" is from 1841. Related: Coaxed; coaxing.