coach has 18 distinct synonyms spread across 6 of its 7 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. WordNet records no antonym for it — antonymy is a relation between word forms rather than concepts, so it is deliberately sparse.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
(sports) someone in charge of training an athlete or a team
a person who gives private instruction (as in singing, acting, etc.)
a carriage pulled by four horses with one driver
a vehicle carrying many passengers; used for public transport
“he always rode the bus to work”
Synonyms, antonyms and the broader and narrower relations for coach come from Princeton University’s WordNet. Full sources and licences.