WordNet records no synonym and no antonym for carpet knight. 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.
a knight who spends his time in luxury and idleness (knighted on the carpet at court rather than on the field of battle)
Synonyms, antonyms and the broader and narrower relations for carpet knight come from Princeton University’s WordNet. Full sources and licences.