WordNet records no synonym and no antonym for deep pockets. 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.
(plural) a source of substantial wealth
“a patron of the arts should have deep pockets”
Synonyms, antonyms and the broader and narrower relations for deep pockets come from Princeton University’s WordNet. Full sources and licences.