Undying rhymes with:
dyeing, dying, applying, belying, buying, complying, crying, decrying, defying, denying, drying, dyeing, dying, eyeing, flying, frying, implying, indemnifying, lying, misapplying, overflying, overlying, plying, prying, relying, replying, retrying, semidrying, shying, sighing, spying, supplying, tieing, trying, tying, underlying, vying
Undying sounds like:
undoing, unending, uniden's, uniting, unwinding, unwitting