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