Heirlooms rhymes with:
handlooms, backrooms, ballrooms, bathrooms, bedrooms, boardrooms, bridegroom's, classrooms, courtrooms, handlooms, legumes, livingrooms, lunchrooms, mailrooms, newsroom's, newsrooms, playrooms, restrooms, showrooms
Heirlooms sounds like:
harlem's, harlin's, harling, herling, herlong, hourlong, hurling