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