Polygynous rhymes with:
indigenous, androgynous, exogenous, homogenous, indigenous, nitrogenous, oleaginous, androgynous, asynchronous, bituminous, brazenness, chitinous, deaconess, exogenous, gelatinous, givenness, gluttonous, homogenous, indigenous, larcenous, luminous, membranous, monotonous, mountainous, mutinous, nitrogenous, nonpoisonous, oleaginous, ominous, outspokenness, patroness, poisonous, ravenous, ruinous, tetanus, titinus, uranus, villainous, voluminous
Polygynous sounds like:
pelagians, pelekunu's, pelican's, pelicans, pillaging, placencia, placing, plagens, plaguing, plaisance, plascencia, plasencia, pleasing, plucinski, plucking, plugging, policeman's, policing, polishing, polyconomics, polygamous, publicizing, publishing, publishing's, publishings, pulsing