Here's what rhymes with irregularity.
                        
                        
                    
                                regularity  rarity  clarity  parity  celerity  verity  polarity  singularity  temerity  hilarity  angularity  capillarity  popularity  prosperity  similarity  solidarity  posterity  granularity  familiarity  sincerity  disparity  peculiarity  dexterity  bipolarity  insincerity  subsidiarity  unfamiliarity  Words that almost rhyme with irregularity
therapy  parody  fidelity  melody  chemotherapy  hypnotherapy  psychotherapy  radiotherapy  physiotherapy  hydrotherapy  readily  legacy  heresy  brevity  leprosy  merrily  warily  wearily  amenity  acerbity  retinae  apparently  carefully  necessity  density  heavily  penalty  seventy  deputy  allegedly  heredity  terribly  serenity  severally  solemnity  verily  sesame  revelry  telemetry  telepathy  velvety  legibly  prayerfully  identity  primarily  chemistry  destiny  integrity  presently  specially  steadily  extremity  heavenly  jealousy  mentally  ordinarily  supremacy  centrally  chemically  peasantry  pleasantly  specialty  carelessly  felony  longevity  pedigree  perplexity  tenancy  clemency  dreadfully  immensity  medically  militarily  recklessly  weaponry  heraldry  inequity  pedantry  pleasantry  unbearably  credibly  nonentity  tenantry  testily  blessedly  devilry  fretfully  negligee  temperately  necessarily  essentially  intensity  tendency  complexity  potentially  pregnancy  secondly  temporarily  voluntarily  arbitrarily  hegemony  ascendancy  customarily  indemnity  sensibly  ascendency  convexity  dentistry  jealously  restlessly  secondarily  breathlessly  flexibly  lamentably  professedly  regretfully  unpleasantly  helpfully  regrettably  unsteadily  vasectomy  successfully  accidentally  momentarily  ostensibly  transparency  helplessly  incessantly  incredibly  tremendously  marvellously  relentlessly  sequentially  splendidly  acceptably  clandestinely  confessedly  incrementally  mastectomy  transparently  impeccably  inclemency  resentfully  tangentially  dependency  discrepancy  incidentally  respectfully  unnecessarily  biochemistry  contentedly  developmentally  exponentially  hysterectomy  insensibly  preferentially  confidentially  indelibly  inexpressibly  providentially  biochemically  existentially  geochemistry  impetuously  instrumentally  respectably  sentimentally  temperamentally  independently  fundamentally  expectancy  experimentally  extraordinarily  conscientiously  environmentally  unsuccessfully  expectantly  quintessentially  tonsillectomy  unacceptably  contemptuously  coincidentally  incontestably  indispensably  superintendency