Latrine rhymes with:
citrine, treen, andreen, brean, breen, citrine, crean, doreen, dufrene, frean, freen, green, greene, ireene, irene, laureen, laurene, lorene, marean, maureen, mcbreen, moreen, onscreen, pilgreen, preen, prien, reen, screen, spreen, sunscreen, tigrean, treen, varin, vidrine
Latrine sounds like:
latrone, leatherman, lederman, leiderman, leiterman, letourneau, letterman, liederman, lutheran, lutterman