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