Infirmities rhymes with:
annuities, authorities', authority's, availabilities, banalities, causalities, cavities, celebrities, celebrity's, charities', christianity's, community's, complexities, complicities, eccentricities, entities, entities', facility's, gratuities, humanities, humanity's, identities, illegalities, immunities, indemnities, inequalities, infidelities, insecurities, instabilities, legalities, localities, majorities, maturities, municipalities, nationalities, necessities, niceties, obscenities, personalities, principalities, rarities, rigidities, sensibilities, sensitivities, trinity's, universities', varity's, vulnerabilities
Infirmities sounds like:
impairments, imprints, informants, informatic, informatics