Here's what rhymes with nonmonetary.
bury dairy cherry berry tarry parry tare barre terry very vary marry monetary fairy merry ferry momentary prairie wary hairy sherry harry nary apiary faerie wherry nondairy military dietary monastery cemetery emissary scary ternary canary unsanitary unwary nonmilitary pessary necessary literary ordinary missionary pulmonary unnecessary commentary coronary solitary urinary sanitary unitary ancillary budgetary corollary estuary honorary mercenary planetary seminary commissary mortuary obituary papillary cautionary dignitary luminary remarry aviary insanitary dromedary equerry lapidary bilberry elderberry topiary plagiary sectary secondary secretary temporary arbitrary customary capillary hereditary imaginary sanctuary adversary legendary maxillary pituitary visionary dysentery salutary sedentary apothecary fiduciary itinerary savagery statuary centenary bacillary beriberi breviary buffoonery legionary actuary cassowary huckleberry humeri nonliterary chokecherry nonhereditary contemporary dictionary stationary subsidiary fragmentary involuntary judiciary tributary veterinary functionary funerary sanguinary stationery interplanetary tutelary concessionary voluptuary uncustomary preliminary vocabulary beneficiary disciplinary pecuniary proprietary reactionary inflationary culinary confectionery epistolary genitourinary paramilitary probationary diversionary eleemosynary recessionary tercentenary evolutionary deflationary expansionary supernumerary constabulary undersecretary geostationary bicentenary elocutionary extraordinary revolutionary discretionary cardiopulmonary exclusionary expeditionary interdisciplinary multidisciplinary counterrevolutionary Words that almost rhyme with nonmonetary
belly jelly deli telly allele smelly underbelly vermicelli barely petty penny jetty teddy bevy jenny many heavy ready fairly rarely steady semi deadly gentry levy antennae heady levee messy belfry deathly machete pebbly tempi testy breathy dressy faery pesky kepi leggy recce sedgy veggie especially twenty healthy gently plenty wealthy lengthy densely fleshy carefree deftly medley sentry sexy sketchy sweaty unfairly unsteady vestry gayety hefty stealthy fidgety tensely trendy aplenty libretti maidenly marquetry thready adeptly lefty wetly already directly assembly scarcely freshly unhealthy frenzy squarely spaghetti coquetry fleshly halfpenny sullenly confetti hostelry effendi preciously woodenly friendly correctly elementary intensely epilepsy immensely intently apoplexy deviancy ineptly indirectly expressly incorrectly unfriendly excellency grotesquely complexly narcolepsy sacredly baronetcy catalepsy reassembly penitently complementary ambivalently cognoscenti confusedly circumspectly equivalently