Balkanize rhymes with:
africanize, americanize, mechanize, africanize, agonize, aluminize, americanize, antagonize, canonize, carbonize, christianize, colonize, communize, demonize, disorganize, euthanize, galvanize, harmonize, hellenize, homogenize, humanize, ionize, lionize, mechanize, organize, patronize, reorganize, revolutionize, scrutinize, suburbanize, synchronize, unionize, urbanize, womanize
Balkanize sounds like:
balchunas, balconies, balkans, balking, belching, belgians, belgium's, bellyaching, bilking, blackening, blackens, blackmun's, blackness, blaesing, blakeney's, blasing, blazing, bleaching, bleakness, blessing, blessings, blocking, blossoming, blossoms, blowguns, bluejeans, blushing, bolognese, bolognesi, bulging, bullishness