Here's what rhymes with nonqueer.
                        
                        
                    
                                gear  year  clear  near  dear  fear  mere  career  beer  rear  deer  peer  shear  sheer  cheer  pier  queer  unclear  mir  feare  leer  veer  vere  vir  yeare  jeer  sear  sere  appear  sphere  adhere  spear  steer  austere  smear  cashier  sneer  cohere  inhere  amir  emir  blear  compeer  cushier  severe  frontier  sincere  financier  revere  veneer  servir  tapir  commandeer  domineer  vizir  besmear  killdeer  marketeer  thornier  rainier  grainier  hornier  leafier  bawdier  cafetiere  cornier  downier  runtier  atmosphere  engineer  interfere  pioneer  volunteer  premier  premiere  reappear  cavalier  insincere  persevere  auctioneer  chandelier  mountaineer  bombardier  gazetteer  gondolier  racketeer  balladeer  chanticleer  brainier  lavalier  junketeer  disappear  hemisphere  brigadier  souvenir  biosphere  chevalier  lithosphere  acyclovir  muleteer  profiteer  bandolier  mesosphere  mutineer  triumvir  exosphere  bandoleer  charioteer  privateer  troposphere  pamphleteer  yesteryear  hydrosphere  bathysphere  electioneer  scrutineer  fusileer  stratosphere  conventioneer  Words that almost rhyme with nonqueer
kill  gill  will  until  till  bill  fill  hill  skill  mill  chill  mil  nil  pill  sill  til  grill  nihil  quill  ville  chil  fil  fille  grille  mille  quelle  rill  untill  vill  wil  wilh  dill  krill  shill  still  drill  thrill  shrill  spill  anil  ftill  trill  twill  frill  gerbil  swill  brill  goodwill  downhill  instill  uphill  benzyl  instil  dunghill  overkill  roadkill  fulfill  distil  distill  freewill  quadrille  overspill  overfill  watermill  pigswill  carboxyl  neutrophil  daffodil  deshabille  dishabille  fiberfill  hydroxyl  eosinophil  espadrille  litre  nitre