Tragedies happen, but Big Mouth's Lee Jong-suk and Im Yoon-ah and Flower of Evil's Lee Joon-gi and Moon Chae-won were happily married couples.

Two of the four couples in SKY Castle (Oh Na-ra and Jo Jae-yoon, Lee Tae-ran and Choi Won-young) had happy marriages.

My Fellow Citizens

Punch, although I don't remember how happy they were 😂

Park Ji-eun, the writer of Crash Landing on You had a lot of hit early works which showed (relatively) loving married couples - Queen of Reversals, Queen of Housewives and My Husband Got a Family.

Her next work, starring Kim Soo-hyun and Kim Ji-won, is apparently a call-back to the 'Queen of...' series and will show them as an already happily married couple!

Reply 1997, the parents were happily married. I'm not sure its been a while.

Park Hee-soon and Chu Ja-hyun in Beautiful World
Ji Seunghyun and Jeon Hye-jin in Search WWW
Kim Hye-soo and Choi Won-young in Under the Queen's Umbrella.

You know what, this is something I'm always talking about wanting more of! My best suggestion is to look to weekend dramas - Five Kids, for instance, has an extremely loving and healthy couple at the centre who get married halfway through the show and have to navigate their new blended family. It's brilliant!

Beautiful World has one of the most beautiful yet realistic depiction of strong and happy marriage (despite all the other tragedy that struck that family).

"that aren’t just the leads’ parents" Hahaha, this does make it harder! All mine are side characters, but I really enjoyed them in these dramas.

First, I would recommend 100 Days My Prince. There is a secondary couple in the village (FL's best friend reluctantly has to get married) and it starts out very much an arranged marriage, but gets cuter as they get to know each other, and definitely by the end it's a happy marriage. They get a good amount of screen time, especially early on when our crown prince is bumbling around trying to be a peasant.

In Vincenzo, two of the residents of Geumga Plaza are a married couple, and they became one of my favorite households in the building. They bicker and are a bit ridiculous (like most of the Geumga Plaza folks) but actually really care about each other and are pretty cute by the end.

The annoying thing about Love is for Suckers is that it had so many adorable characters and storylines while not being a very good drama at all. @vienibenmio has already done us all a favor and cut out the chef/webtoon artist scenes, but now I also want a cut of all the bits with Park Dae-sik and Oh Hye-jin. They were my favorite thing about the show for a few weeks of watching, and I loved how much they were a team and always on the same page. Their struggle to conceive is such a heartbreaking one, but I loved to see them support each other during it.

One of my favourite drama of last year was web drama The Killer is Also Romantic and the show actually begins with the leads marrying for love. It definitely features the most steamy kisses of last year as well.

Happiness with Park Hyung-shik and Han Hyo-joo 😍 ha ha ha
I like the parent couple in Minari, Happily married doesn't mean they can't argue. Arguing is only mean despite all said and done, they know and sure, they won't leave each other, right?

This is a good question! But there are not many happily married couples featured as leads.
Skycastle, of course, has already been mentioned. I'm not sure if they qualify as "leads," but the parents in Father Is Strange, both sets of parents in It’s Beautiful Now. Maybe also Five (is) Enough?

Cha Eunho and Kang Dan-i in Romance is a Bonus Book.
(Especially when Lee Jong-suk, actor behind Cha, is comparing her to his newly revealed girlfriend)
(Sorry, I am just sad, yet happy about them)

Not really what it sounds like you’re looking for but in Tunnel the lead is happily married and wants to get back to his wife (after he has travelled through time 😅)

This is a good one! @panshel has a good one with Flower of Evil. I'd also gladly recommend A Thousand Days' Promise. With Soo Ae and Kim Rae-won as the lovely couple. I watched it when it came out 11 years ago and cried buckets. Sadly there was a horrible ilness in play, but the couple were really happily married and very much in love.

Why has no one mentioned Tomorrow with you? It has one of the best marriages in kdramaland. It stars lee he Hoon and shin min ah

Flower of Evil.

The FL's parents in MY ID IS GANGNAM BEAUTY had a very strong marriage. In contrast, the ML's parents were divorced.

One of the things which set the show apart from most college romcoms is that the parents were in fact a major part of the story.

NAVILLERA (2019): Husband Deok-chul (Park In-hwan) and wife Hae-nam (Na Moon-hee). Long married loving couple played by two wonderful character actors. They were just great together in a great drama.

Would Hi, Bye Mama count? From what we saw, they had a beautiful marriage before her untimely death. And his second marriage was also respectful and loving.

Goblin Shin (eventually) married Eun-tak and they were a very happy married couple... for the time they had.

Lee Sung-Min and Oh Yoon-Hong in Misaeng: Incomplete Life. Despite his working incredibly long hours and occasionally coming home dead drunk, they were a loving, supportive couple as well as terrific parents.

No one has mentioned this yet - the President couple in Designated Survivor! A beautiful couple inside out.

Aside from Flower of Evil couple, there was also the Undercover couple played by Ji Jin Hee and Kim Hyun Joo. They were happily married too. Cute couple.

Soundtrack #1 was disappointing, but the married couple who owned a bar was quite cute.

The female lead's parents in Another Oh Hae Young. Solid supportive couple and parents. In contrast to the male lead's terrible mother.

Racket Boys : the parents formed a nice couple. They took care of a lot of kids!

Sae hee and jiho from because this is my first life. Technically they are, thought towards the end of the series.

The elderly proprietor of Laurel Tree Tailors and his wife seem to have enjoyed a long and truly loving marriage—though I thought it was kind of cruel of him to hide the reason for his sudden disappearance and the fact that he was losing his eyesight.

Pick me! Pick me! I had one right off the top of my head:

Welcome2Life - it's hilarious. They aren't married in the first universe, but that changes in episode one so I think it counts.

Other than that, I second Flower of Evil, which is AWESOME even though they play on the idea that maybe they shouldn't trust each other so much.

Father Is Strange.
Memory (Lee Sung Min's second marriage).
And if I recall correctly, a couple of happy contract marriages, Contract Marriage and 1% of Anything.

Happiness!.
Park Hyung Sik and Han Hyo Joo were damn goals as married couples specially the kind of rapport they shared made it even more special watch. I'm sucker for these kinda romances <333

The 2012 drama My Husband Got A Family/You Who Rolled in Unexpectedly, with Kim Nam Joo and Yoo Joon Sang. Female Lead marries Male Lead because he doesn't have a Korean family, just for them to discover that the neighbors are his missing family (he got "lost" as a child and adopted by an American couple). The leads have a great relationship throughout the whole 58 episode drama.

So I'm binging the Cursed right now and at episode 9 the married couple is still going strong. I'm hoping it stays that way :)