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