Alkire rhymes with:
skier, admire, afire, aspire, barbed-wire, beijer, dire, dwire, eir, expire, frymire, gire, guire, gyr, hyre, inquire, inspire, ire, lyre, maguire, martyre, mcguire, mcgwire, mcquire, mire, myre, o'dwyer, perspire, quire, reacquire, rehire, retire, safire, schreyer, scire, shire, skier, smyre, spire, squire, striar, swire, tyre, wyre
Alkire sounds like:
alcazar, alcocer, alegre, alegria, aleshire, algar, alger, algeria, alguire, allegory, allegra, allegro, allgaier, allgeier, allgeyer