WordNet records no synonym and no antonym for apple of discord. It is the only member of its synset, which is common for technical, taxonomic and single-sense vocabulary — there is no other English word that means the same thing. The broader and narrower terms below are the useful relations in that case.
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.
(classical mythology) a golden apple thrown into a banquet of the gods by Eris (goddess of discord--who had not been invited); the apple had `for the fairest' written on it and Hera and Athena and Aphrodite all claimed it; when Paris (prince of Troy) awarded it to Aphrodite it began a chain of events that led to the Trojan War
Synonyms, antonyms and the broader and narrower relations for apple of discord come from Princeton University’s WordNet. Full sources and licences.