quiet has 27 distinct synonyms spread across 10 of its 13 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. Its 3 recorded opposites are unquiet, noisy, active.
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.
characterized by an absence or near absence of agitation or activity
“a quiet life”
free of noise or uproar; or making little if any sound
“a quiet audience at the concert”
(of the sun) characterized by a low level of surface phenomena, such as sunspots
the absence of sound
“he needed silence in order to sleep”
a disposition free from stress or emotion
become quiet or quieter
“The audience fell silent when the speaker entered”
make calm or still
“quiet the dragons of worry and fear”
with little or no activity or no agitation (`quiet' is a nonstandard variant for `quietly')
“her hands rested quietly in her lap”
Synonyms, antonyms and the broader and narrower relations for quiet come from Princeton University’s WordNet. Full sources and licences.