curse has 26 distinct synonyms spread across 8 of its 9 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 bless.
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.
an appeal to some supernatural power to inflict evil on someone or some group
heap obscenities upon
“The taxi driver who felt he didn't get a high enough tip cursed the passenger”
exclude from a church or a religious community
“The gay priest was excommunicated when he married his partner”
Synonyms, antonyms and the broader and narrower relations for curse come from Princeton University’s WordNet. Full sources and licences.