Diaconate rhymes with:
affectionate, baronet, bicarbonate, cabinet, compassionate, coordinate, definite, dispassionate, extortionate, fortunate, geminate, indefinite, indiscriminate, infinite, innominate, laminate, nominate, nondiscriminate, obstinate, passionate, proportionate, sultanate, unfortunate
Diaconate sounds like:
d'genetta, dachshund, decandia, decant, decent, dechant, decimate, decimated, deigned, desanti, desanto, descend, descended, descent, designate, designated, designed, desmet, desmith, desmond, dessent, detachment, dicomed, dignity, disanti, disanto, discount, discounted, disjoint, disjointed, dismayed, disowned, disseminate, disseminated, dissent, dissented, dissonant, disunity, docent, document, documenta, documented, doesn't, doughnut, dushyanth