WordNet records no synonym and no antonym for rain check. 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.
a promise that an unaccepted offer will be renewed in the future
a ticket stub entitling the holder to admission to a future event if the scheduled event was cancelled due to rain
Synonyms, antonyms and the broader and narrower relations for rain check come from Princeton University’s WordNet. Full sources and licences.