I'm not a native speaker but that doesn't sound good to me. I'd say Would you like a cup of coffee? "Would" doesn't usually work well with "have" at least not in this question.
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BamtoriFor making a polite offer or invitation, you use the modal 'will' like, "Will you have a cup of coffee?" Then can I say, "Would you have a cup of coffee?" to make a more polite offer?This must be frustrating for you. Your reasoning is good, but it just doesn't work as you expected for this situation.