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