WordNet records no synonym and no antonym for fountain of youth. 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 fountain described in folk tales as able to make people young again
“Ponce de Leon discovered Florida while searching for the Fountain of Youth”
Synonyms, antonyms and the broader and narrower relations for fountain of youth come from Princeton University’s WordNet. Full sources and licences.