sinking has 1 distinct synonym spread across 1 of its 3 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.
a descent as through liquid (especially through water)
“they still talk about the sinking of the Titanic”
a slow fall or decline (as for lack of strength)
“after several hours of sinking an unexpected rally rescued the market”
a feeling caused by uneasiness or apprehension
“with a sinking heart”
Synonyms, antonyms and the broader and narrower relations for sinking come from Princeton University’s WordNet. Full sources and licences.