Priam's rhymes with:
abrahams, amsterdam's, cunningham's, diagrams, electrocardiograms, histograms, holograms, kilograms, logjams, logograms, mailgrams, mammograms, micrograms, milligrams, oxfam's, polygram's, program's, programs, programs', reprograms, sonograms, telegrams, westerdam's
Priam's sounds like:
pairing, papering, papernick, papier-mache, paramax, paramus, paranoiac, paring, parnassus, parnes, parness, peering, peppering, permanence, pernice, pernicious, perrins, pharaonic, pharmacia, pharmacies, pharmacy, pharynx, pheromones, poring, pouring, powering, prance, prances, prange, prank, pranks, prawns, praying, prearrange, prearranges, preeminence, preening, premise, premises, premiums, prensa, preying, primack, primacy, prime's, primeaux, primeco, primenews, primes, priming, primo's, primus, prince, prince's, princes, princess, princess', princess's, princesses, pring, prinkey, prinos, prins, prinz, prinz's, prominence, prominences, promiscuous, promise, promises, promos, proms, promus, prong, prongs, pronounce, pronounces, pronouns, prunes, pruning, prying, purring, pyrenees, pyrenees'