Irrelevancy rhymes with:
relevancy, relevancy, relevancy, relevancy, conservancy, insolvency, relevancy, solvency, absorbency, accountancy, agency, ascendancy, ascendency, buoyancy, clemency, cogency, complacency, conservancy, consistency, constancy, constituency, consultancy, contingency, counterinsurgency, currency, decency, deficiency, delancey, delancy, delinquency, dependency, despondency, discrepancy, dormancy, efficiency, emergency, equivalency, exigency, expectancy, expediency, fluency, frequency, hesitancy, immunodeficiency, incompetency, inconsistency, inconstancy, incumbency, indecency, inefficiency, infancy, infrequency, insolvency, insurgency, interagency, latency, leniency, malignancy, militancy, nonemergency, occupancy, poignancy, potency, pregnancy, presidency, proficiency, prudency, redundancy, regency, relevancy, residency, resiliency, resurgency, self-sufficiency, solvency, stridency, stringency, sufficiency, surrency, tenancy, tendency, transparency, truancy, urgency, vacancy, vagrancy, vibrancy