WordNet records no synonym and no antonym for double negative. It is the only member of each of its synsets, 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.
an affirmative constructed from two negatives
“A not unwelcome outcome”
a grammatically substandard but emphatic negative
“I don't never go”
Synonyms, antonyms and the broader and narrower relations for double negative come from Princeton University’s WordNet. Full sources and licences.