Jamaica's rhymes with:
africa's, alaska's, alyeska's, america's, americas, angelicas, antarctica's, babushkas, balukas, bankamerica's, bazookas, biotechnica's, clucas, coastamerica's, corsicas, delucas, ditka's, doukas, dykas, fazekas, formica's, gikas, hanukkah's, hanukkahs, heikes, hosoka's, iacocca's, incas, ithaca's, jessica's, joncas, kafka's, kazlauskas, kiska's, klukas, labianca's, lanka's, latkas, lekas, lukas, luxottica's, marseca's, mazurkas, mclucas, mecca's, metallica's, minorco's, mochas, monica's, musica's, nebraska's, pagliuca's, palca's, palinkas, parkas, petrauskas, picas, polkas, primerica's, puskas, rebecca's, replicas, rica's, savickas, swastikas, tonka's, topeka's, trakas, transamerica's, tunica's, vodkas, westamerica's, zeneca's, zukas
Jamaica's sounds like:
jacking, jackson's, jacksonians, jacksons, jaenicke, jahnke, jahns, jaime's, jaimes, jam's, jamaica, james, james', james's, jamesway, jamie's, jamming, jammu's, jams, jan's, janacek, janachowski, janak, janas, janca, janco, janczak, jane's, janecek, janeczko, janek, janes, jang, janiak, janice, janicek, janick, janicke, janicki, janiga, janik, janikowski, janis, janisch, janish, janiszewski, jank, janka, janke, jankiewicz, janko, jankowiak, jankowski, janning, jannock, janos, janosik, janoski, janosko, janosky, janousek, janowiak, janowicz, janowski, jans, jansa, jansky, janus, janusz, januszewski, janz, jasinowski, jasinski, jason's, jaymes, jaynes, jean's, jeanes, jeans, jem's, jencks, jenks, jenn's, jenness, jenning, jennings, jenny's, jens, jeong, jewishness, jiang, jiang's, jiangsu, jim's, jimenez, jiminez, jimmy's, jines, jing, jinks, jinx, joachim's, joachims, jockeying, joens, jogging, johannes, johanning, johanns, john's, johnnie's, johnny's, johns, johns's, johnsey, joines, joining, joins, jokhang, joking, jon's, jonas, joncas, jones, jones', jones's, joneses, jong, joong, joying, joynes, juang, juhnke, jumanji, junco, june's, junejo, junek, junes, jung, jung's, junge, junius, junji, junk, junkie, junkies, junky, juno's, jynx