Uni rhymes with:
cuny, kuney, muni, munni, puny, bruney, bruni, bunni, clooney, cluny, cooney, cuhney, cuny, fortuny, katuni, kuney, looney, loony, marooney, mccluney, mooney, moonie, muni, munni, nooney, puny, rooney, shigekuni, suni, sunni
Uni sounds like:
ueno, um, uma, umana, umm, un, una, uneo, union, uno, unum, unwin, uyeno