Merry Christmas

A frequently asked question is how to wish Merry Christmas in Klingon. The problem of this question is that Klingons don't celebrate this day.

It's not possible to translate "Merry Christmas" into Klingon literally. First, there is no Klingon word for "Christmas", so the English word will just get respelled to approximate a Klingon "accent". The canon transliteration is QISmaS. Second, there's no simple Klingon term to represent the connotation of this use of "Merry", which implies festivities and cheerfulness and generally high levels of good will toward all.(1)

Canon solutions

Maltz thought, it seems ridiculous to ask this question, but offered QISmaS yItIv! (enjoy Christmas), QISmaS DatIvjaj! (May you enjoy Christmas) and QISmaS botIvjaj! (may you all enjoy Christmas) as alternatives.(2)

"Happy" Christmas?

There is one phrase around on the web which looks correct at first sight, but is not:

QISmaS Quch Daghajjaj

When translated literally, this says "May you have a happy Christmas". This phrase is grammatically correct, but it carries several problems:

The verb Quch "be happy" can only be applied as an emotion sensed by beings. In other words, a holiday cannot be happy.
The verb ghaj "have, possess" really refers to the possession of something. You can have a dog, you can have a lot of money, but you surely cannot possess a holiday.

So it is definitely not recommended to use this sentence.

The above phrase did not originate from an online translator: It first appeared in 2001 (3) or even earlier, many years before Bing was launched. Also, the term QISmaS was already used even before it was canon. The phrase constantly re-appeares in 2004, 2006 (4) and 2009 (5). It was also used on a wrapping paper sold on etsy.com in 2010, but is not avilable any longer.

Canon statement

On qepHom 2021, Marc Okrand confirmed that Christmas can not be Quch and that ghaj is not a good word choice:

LL: During the days after the qepHom, I stumbled over a phrase that had been around the web for a long time and is used very often. It somehow felt a bit awkward to me though. The phrase is: QISmaS Quch Daghajjaj. It is obviously supposed to mean "May you have a happy Christmas". But even though it seems to follow grammatical rules, I wondered: Can Christmas be Quch? And can you really ghaj that Christmas?
MO: This is something that a Klingon (on Qo'noS and/or talking to other Klingons) is unlikely to say. It's a calque from Federation Standard and, presumably, in speaking with Federation folks. So the expression is, by its very nature, an odd one and shouldn't be expected to necessarily be an example of "proper" or everyday Klingon. QISmaS Quch is a well-formed phrase (that is, it's a noun followed by a verb expressing a state or quality, so it follows the rules). As such, you can use it as the object of a sentence (as in the phrase you're asking about), and you can also use it as the subject, as in something like mon QISmaS Quch. All of these phrases exemplify anthropomorphizing — or Klingono-morphizing? — but such formations can be okay in context. (The paq'batlh, for instance, talks about two hearts that "knew emptiness" and "fought the storm," though we only have these phrases in no' Hol.) So one can make sense out of QISmaS Quch. The question is, does it mean what the web contributors that you refer to intend?
You're right that ghaj refers to the possession of something (dogs or money, in your example). But it can also be used to express displaying or being characterized by a particular quality or feature, as in quv ghaj or tlham ghaj (in both its literal and slang senses). ghaj and English "have" don't match up entirely, of course. For example, where "have" is used in English to mean "experience" or "undergo" ("have a nice time"), Klingon may make use of SIQ or other formations; ghu ghaj does not mean to give birth; and you would not place an order in a Klingon restaurant by saying qagh vIghaj (nor would you say that phrase when the food arrives and the server has forgotten who gets what).
LL: I agree that this Christmas greeting is not a Klingon thing, but we are dirfting of. Let's focus on the grammar only. My first straight question: can the verb Quch be applied to events or days? Klingons certainly do not celebrate Christmas, but I'm sure they have other events. Does QI'lop Quch make any sense? You recently told me that a voice can not be angry, so ghogh QeH is not okay. So I assume ghogh Quch also is not. Now what about a "happy birthday"? Is that a qoS Quch? So the question basically is: Is the word Quch restricted to human emotions? Honestly, summarizing this, I am mostly concerned about the grammatical usage of the verb Quch and the correctness of the sentence. What would a Klingon understand when they hear this sentence?
MO: There's a famous English sentence in linguistics: "Colorless green ideas sleep furiously." (6)
It's perfectly grammatical, but seman-tically it's nonsense. Same for QISmaS Quch: it follows the grammatical rules, but it's nonsense, specifically because non-sentient things (like holidays) don't/can't experience emotions.
One could be very imaginative, I suppose, and come up with a scenario in which a construction like QISmaS Quch might be used. Let's say you wrote a story in which QI'lop was a character and felt left out because none of the other holidays ever wanted QI'lop to play with them. Then, one day, all of the other holidays invited poor little QI'lop to join in. QI'lop was so happy! Quch QI'lop! mon QI'lop Quch. (QI'lop Quch could be best-selling children's book.) In order for this to work, of course, you have to treat QI'lop and the other holidays as characters, as if they were human or Klingon or some other sentient species.
In short, QISmaS Quch does not mean that somebody's experience during the Christmas season is merry (whether you can ghaj it or not). And though in a poetic or other literary context people might do interesting things, for regular, everyday Klingon, your instincts about Quch are correct.
(qepHom 2021)