Unfailing rhymes with:
failing, ailing, assailing, ayling, bailing, baling, curtailing, derailing, detailing, emailing, entailing, failing, flailing, grayling, hailing, impaling, inhaling, jailing, mailing, nailing, prevailing, railing, regaling, sailing, saling, scaling, surveilling, tailing, trailing, unavailing, unveiling, veiling, wailing, whaling
Unfailing sounds like:
unappealing, unavailing, unbalance, unfeeling, unveiling