Imaginary rhymes with:
cardiopulmonary, cautionary, centenary, concessionary, confectionary, confectionery, coronary, counterrevolutionary, deflationary, dictionary, disciplinary, discretionary, disinflationary, diversionary, evolutionary, exclusionary, expansionary, expeditionary, extraordinary, functionary, illusionary, inflationary, interdisciplinary, luminary, mercenary, missionary, noninflationary, ordinary, preliminary, probationary, pulmonary, reactionary, recessionary, revolutionary, seminary, stationary, stationery, urinary, veterinary, visionary
Imaginary sounds like:
imagineer, ingemar, ingmar, ingmire