stability has 2 distinct synonyms spread across 2 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. Its one recorded opposite is instability.
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.
the quality or attribute of being firm and steadfast
a stable order (especially of society)
the quality of being enduring and free from change or variation
“early mariners relied on the constancy of the trade winds”
Synonyms, antonyms and the broader and narrower relations for stability come from Princeton University’s WordNet. Full sources and licences.