Here's what rhymes with counteu.
to who you do two new too true due knew blue drew du u blew coup qu shoe zu dew lieu shew su sue tu vous chew deux fu lu rue zoo brew bu hu ju jus ku loo mu nu peu pew pu seu shu sou vu woo yew yu boo chou chu coo cou doo ewe feu gu ru shou thu tue tzu vou wou wu goo moo pooh poo shoo gnu roux thew whew through few view grew que crew pursue threw flew q anew clue cue glue hue queue cu flue slew stew taboo untrue adieu ado flu piu tattoo thru beaucoup fue hew mieux outdo shrew sprue vue clew imbue mew strew spew endue indue slue phew booboo achoo into screw bamboo canoe renew undue accrue debut ensue subdue undo construe jusqu skew eschew kangaroo vnto outgrew redo halloo valuer fondue zebu kazoo muumuu wazoo atishoo review interview withdrew avenue rendezvous retinue caribou overdue revue shampoo sinew askew overdo ballyhoo cockatoo honeydew bugaboo foreknew marabou peekaboo bestrew buckaroo overshoe prevue overdrew regrew revenue hitherto overview residue overthrew overflew superglue overgrew barbecue hullabaloo misconstrue barbeque