Picture someone by a sofa, talking softly to whatever is hiding under it. Nothing is being pulled, ordered or argued with. There is a warm voice, a small offer, a wait, and then the same thing again. Coax is that whole method: the other side does not want to move, and you change that with patience instead of strength.
From the word’s history
The verb first appears in the 1580s in the phrase to make a coax of someone, built on an older noun coax or cokes meaning 'a fool' — that is, to work on a person with soft words. The origin of that noun is unclear, and the modern spelling dates from 1706.
這個動詞最早出現在一五八〇年代的說法 to make a coax of somebody，背後是更早的名詞 coax／cokes，意思是「傻瓜」——也就是用好聽話把人擺弄。那個名詞本身來歷不明。今天的拼法從一七〇六年開始。這條線索留下的味道是：好話有時候是真心，有時候只是手段。
Wiktionary entry 'coax' (verb, etymology 1; packet source_ref kaikki:3f6f69a190036ae4:822212748)
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