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