Here's what rhymes with perfunctionary.
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belly allele jelly smelly deli telly vermicelli underbelly many messy heavy ready fairly rarely barely semi petty levy penny antennae heady levee medley unfairly jetty teddy bevy faery jenny kepi leggy recce sedgy veggie healthy steady wealthy deadly lengthy gentry unhealthy fleshy squarely carefree sentry sexy sketchy spaghetti sweaty unsteady vestry belfry deathly gayety hefty machete sullenly confetti fidgety pebbly tempi testy breathy dressy pesky thready lefty wetly already especially twenty assembly scarcely elementary gently plenty freshly immensely densely frenzy deftly coquetry fleshly halfpenny stealthy hostelry tensely trendy aplenty libretti maidenly marquetry adeptly effendi ineptly directly friendly correctly complementary expressly intensely epilepsy intently unfriendly excellency sacredly baronetcy preciously woodenly indirectly incorrectly apoplexy grotesquely complexly narcolepsy catalepsy cognoscenti deviancy reassembly confusedly equivalently ambivalently circumspectly penitently