Countenance rhymes with:
incontinence, maintenance, abstinence, incontinence, maintenance, sustenance, abstinence, chrominance, dissonance, dominance, eminence, immanence, imminence, incontinence, luminance, maintenance, ordinance, permanence, predominance, preeminence, prominence, provenance, resonance, sustenance
Countenance sounds like:
camden's, canadian's, canadians, canadians', canteens, cantonese, cantons, cementing, centimes, chanting, chintung, comedian's, comedians, commanding, commending, commenting, committing, commuting, condemning, condemns, condense, conditioning, conditions, condominiums, condoms, condones, condoning, connotations, containing, contains, continuance, continuances, continues, continuing, continuous, countdowns, countenances, counting