Umpteenth rhymes with:
absinthe, amaranth, billionth, coelacanth, corinth, cynth, drenth, dushyanth, eighteenth, eleventh, eranthe, fifteenth, fourteenth, helminth, hyacinth, hyacinthe, jacinth, jacinthe, labyrinth, millionth, month, nineteenth, ninth, nth, plinth, rhodanthe, seventeenth, seventh, sixteenth, tenth, thirteenth, threemonth