Argonaut's rhymes with:
argonauts, argonauts, argonauts, argonauts, astronauts, astronauts', cosmonauts, cosmonauts', argonauts, astronauts, astronauts', cosmonauts, cosmonauts'
Argonaut's sounds like:
aerosmith's, arachnids, archimedes, argonauts, argument's, arguments, arraignments, arrowsmith's