Here's what rhymes with establye.
apply dry lie try ly ply rye lye pry tri trie wry lai luy pri by my high why 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 comply defy spy butterfly underlie decry pupae untie sty aquae bonsai firefly retry triply amebae misapply stupefy stye turfy lanai ripply thereby justify nearby satisfy whereby hereby multiply certify goodbye alibi samurai standby terrify typify amoebae descry edify overlie oversupply resupply deify mystify stultify ultrahigh blowfly petrify overfly barfly hyperbolae drachmai speechify banzais yuppify occupy stimuli modify nuclei specify alkali simplify testify verify notify purify alveoli amplify fortify nullify pacify ratify unify beautify lullaby termini codify mollify ramify vilify acidify ossify stratify vivify horrify dissatisfy scurfy versify mummify prettify shanghai vitrify beatify gentrify overbuy syllabify dandify identify clarify qualify classify signify exemplify glorify gratify rectify falsify solidify crucify dignify liquefy mortify personify demystify dragonfly electrify calcify reunify revivify liquify scarify refortify intensify quantify diversify magnify disqualify indemnify objectify detoxify preoccupy emulsify cumuli declassify misidentify oversimplify reclassify solemnify transmogrify