Perishing rhymes with:
cherishing, cherishing, impoverishing, abolishing, accomplishing, admonishing, anguishing, astonishing, banishing, brandishing, cherishing, demolishing, diminishing, distinguishing, embellishing, establishing, extinguishing, finishing, flourishing, furbishing, furnishing, impoverishing, languishing, lavishing, nourishing, photofinishing, polishing, publishing, punishing, ravishing, reestablishing, refinishing, refurbishing, relinquishing, relishing, replenishing, skirmishing, tarnishing, vanishing
Perishing sounds like:
parisians, parking, parkins, parsimonious, parsing, parsonage, parsonages, parsons, pearson's, perchance, perking, perkins, perkins', perkins's, pershing, pershing's, pershings, persians, persing, person's, personic, personics, persons, persuasions, perusing, phrasing, piercing, praising, preaching, preakness, pregnancies, pregnancy, presaging, prescience, presence, presences, pressing, presumes, presuming, pricing, pricings, prisms, prison's, prisons, processing, processions, prognoses, prognosis, prusinski, purchasing, purging, pursuing