Here's what rhymes with rigoroufly.
lie fly fry ly rye sly lye wry lai luy slier by my high why apply die dry thy try y buy cry sky guy tie vi hi shy sigh bi bye chi dye fi hy nigh pi pie spy thai thigh vie dei ply psi quae ty wir awry hai mai muy nai pry tri trie cy fy kai mei pri sy tai thei wai phi sty spry stye overfly supply thereby rely hereby belie untie overlie aquae firefly amebae lanai reply deny imply nearby whereby comply defy verify butterfly underlie alibi alveoli samurai decry pupae amoebae descry oversupply vilify bonsai ossify retry blowfly horrify turfy scurfy versify barfly shanghai ripply overbuy justify occupy satisfy nuclei alkali certify glorify goodbye notify fortify nullify pacify ratify rectify unify falsify lullaby terrify codify edify liquefy mollify ramify resupply acidify deify dragonfly triply ultrahigh vivify misapply stupefy liquify scarify mummify vitrify drachmai banzais yuppify stimuli clarify modify multiply qualify specify classify signify simplify testify gratify purify amplify standby beautify solidify termini typify crucify dignify mortify personify electrify mystify stratify stultify calcify emulsify petrify reunify cumuli dissatisfy hyperbolae prettify refortify speechify syllabify exemplify intensify quantify diversify magnify oversimplify reclassify revivify declassify beatify gentrify dandify solemnify identify disqualify indemnify objectify demystify detoxify preoccupy transmogrify misidentify