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