It seems to me that in this context ευχή refers not to a wish that you are making for yourself, but a wish (blessing, well-wishing) for someone else, be it on festive or on other occasions. The Greeks have a lot of these wishes/greetings, and you will hear them often (here is a nice list). So what is actually meant would be such a wish made on a joyful occasion, or at least a wish brought forth in a joyful way - expressing the joy and the positive feelings of the well-wisher.
Why would you want to translate this as "a good wish" when the Greek means "happy". We are translating not interpreting. Just follow these guidelines:
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Jaye & nestarees: "Sending glad wishes" (or "...every glad wish") is most definitely a time-honored English phrase. The internet is awash with examples of greeting cards and needlepoint samplers with this precise (if old-fashioned) sentiment. https://www.flickr.com/photos/striderv/33390586372