Basenji rhymes with:
benjy, kenji, angi, angie, angy, bangee, benjy, bungee, bungey, cherrapunji, digangi, dingy, dungey, evangi, gangi, grungy, jumanji, junji, kanji, kenji, mangy, rangy, solangi, songy, sonji, spongy, stingy, twangy, vangy
Basenji sounds like:
backing, bacon's, bafokeng, bagginess, bagging, baginski, baking, baoguang, bashing, basim's, basing, basins, basinski, basking, baskins, beaching, beacons, beakman's, beckoning, beckons, becomes, becoming, beecham's, begging, begin's, beginning, beginnings, begins, begnoche, begonias, beijing, beijing's, bekins, beseeching, besieging, bicking, biggins, bigness, biking, bikinis, biogen's, bioscience, biosciences, bizango, bochenek, bogging, bojanowski, bojenka, booking, bookings, boozing, bosnia's, bosnian's, bosnians, bosnias, bowsing, boxing, boxing's, boykins, buchanan's, buchanans, bucking, buckskins, buczynski, buesing, bugging, bushings, bushong, bushwhacking, business, business', business's, businesses, businesses', busing, bussing, buzzing, bygones, bypassing