Here's what rhymes with counterman.
man nan can than ran van ban fan pan tan dan shan kan kann san dann gan lan japan began plan clan scan span bran gran sedan divan journeyman middleman rattan cyan flan anchorman saran fisherman overran catamaran handyman nurseryman outran bogeyman turbofan weatherman paperhanger boogeyman minuteman businessman caravan newspaperman serviceman minivan radioman assemblyman Words that almost rhyme with counterman
nam hang dam damn gang rang sang jam lamb bang cam ham ram sham yang lam lang langue pang tam tang chang fang yam dang jamb wham gram slang swam clam harangue slam tram clang cram dram gramme boomerang pram scam spam glam flambe prang diagram sprang diaphragm exam epigram overhang buckram cofferdam doorjamb scram shebang rehang telegram milligram monogram quondam anagram pentagram grandam centigram whizzbang histogram kilogram diazepam hologram mammogram cablegram ideogram sonogram cardiogram orangutang kissogram radiogram hexagram parallelogram electrocardiogram electroencephalogram hasn