The two that immediately come to mind are rom coms:
Marriage not dating
Business proposal

Because This is My First Life
My Girl (except it's a siblings contract I think)
Full House

We have Quite a few here, don’t we? but I can’t seem to recollect.

Because this is my first life and Something about 1% comes to mind.
Both of these I quite liked.

In the order of how I enjoyed them :-
Because This Life is My First.
Marriage Contract.
The Prime Minister and I.
The Beauty Inside.
Perfume.

Because This Is My First Life
Couple or Trouble (remake of the Goldie Hawn/Kurt Russell Classic "Overboard")
Full House
Her Private Life - has contract dating in the beginning
Marriage, Not Dating
Mary Stayed Out All Night

Fated to Love You - Taiwan version was first, but there's also a Korean remake and a Chinese remake.

Full House, Happiness, Her Private Life and Crazy Love in addition to the ones that were already mentioned

Contract Marriages:

Marriage Contract - a melo but so very good

Full House - the OG

Happiness - FL marries her long time friend because she desperately wants an apartment of her own. Trade off being that it’s a zombie infested building

Once Again - an interesting spin, a divorced couple too cowardly to tell their respective families pretend they are still together

Forced/Arranged Marriages:

Delightful Girl Chun-hyang - they get married when they are still in high-school, I honestly don’t remember why, I think they were misunderstood as spending the night together?

Mask - a chaebol arranged marriage with a doppelgänger twist!

Accidental Pregnancies:

Fated To Love You - our two protagonists get drugged and sleep together, they obviously have a surprise pregnancy and get hitched.

Ojakkyo Brothers - in a similar vein but instead they get drunk and get pregnant and are the secondary couple in this family drama

Contract/Fake Dating:

Coffee Prince - ummm it’s a little offensive but ML asks FL (who he thinks is a dude) to be in a fake gay relationship so that he can put an end his family’s blind date obligations

Stranger and me/man living at my house counts i think. Fl finds out her mom who passed away was in a contract marriage and now has to live with her 'step father'

Since most of the K-dramas have been named, I'll go slightly further afield and recommend some J-dramas with very elaborate marriage contract plots:
1. Marry Me! - Marriage contract under a government program (yes really!)
2. Shanai Marriage Honey - Contract marriage between co-workers who don't know they're co-workers
3. Only Just Married - Fake marriage for...reasons...

I think that many of my favorite romcoms fall into this category, and I would recommend all of these very highly, and I have arranged them in order from TRULY great down to really good:

BECAUSE THIS IS MY FIRST LIFE

BUSINESS PROPOSAL

MARRAIGE NOT DATING

1% OF SOMETHING which was a remake of 1% OF SOMETHING (both are really good).

FATED TO LOVE YOU a remake of a good T-drama, but Jang Nara nailed it, and the re-make is actually better. It is in my opinion the very best version of story that has been re-made elsewhere as well.

FULL HOUSE

Because this is My First Life has a double dose - one contract marriage, and one contract dating (FL's friend is contract-dating the ML's friend/boss)... and one scene where the inevitable discovery of the other's contract happens in a paper shuffle.

Marriage Contract. I quite little offhand watch, it's always somehow stayed with me and was deeper and richer than I expected it to be.

I love a good contract marriage. I also love how the reasons they enter into one often tell us about the culture. Because this is my first life - finding housing is a major stressor on young people in Seoul. Chinese drama, Time to Fall in Love - they marry to make the elders (his grandmother) happy. And in the Netflix movie Purple Hearts set in the U.S. what could make people need to enter a contract marriage? Health insurance.

How serendipitous! I just finished 1% of Anything/something and loved it. A couple forced kisses, but otherwise enjoyable. Lots of unforced consensual kissing otherwise. And good kissing too! 😆 I’ve got kissing on the brain apparently.

Recommended:
Because this is my first life: exceptional till episode 14. Stop there. No need to go further.
1% of anything (newer one): enjoyable.
Marriage not dating: quite enjoyable and even insightful in certain scenes.
A business proposal: Breezy till episode 10.
Happiness: Added bonus of friends to lovers
The romance of tiger and rose: Utter fun.

Avoid:
Goong: Teen marriage even involves adult forcing teenager to do something they shouldn’t.
Well intended love: Just run. This drama has no business of being in existence.
Somewhere in between:
Sassy Girl, Chun Hyang (2005): I have no recollection of the drama but I wasn’t offended by it.
Fated to love you: Essential for Jang Na ra and Jang Hyuk admirers.
To fly with you: Lead pair is quite charismatic.
Crazy love: Only for Kim Jae Wook fans
Unforgettable love: For fans of cute kids

Creating Destiny, Lie to Me, Mask, Warm and Cozy, Ojakygo Brothers, and Delightful Girl, Choon Hyang are few faves that come to mind.

Everything I was going to mention has already been listed, so I’m just going to throw this out there… To All the Boys I’ve Loved Before.

I know, I know. Not a K-drama, like, at all. In fact, it is very much an American movie, BUT it does have contract dating and the female lead’s character is half-Korean (even though Lana Candor is not—still love her). It was also fun to watch and, I think, had the right amount of tropiness and gave out all the right types of feels to be included here.

It’s not amazing but it’s an ok webdrama - Ending Again. Tbh I remember very little about it (my notes in my drama list say “it was fine” 😅), it’s a fake marriage to qualify for a newlywed apartment.

Outside of Korean dramas, cdrama Cute Programmer has a contract marriage, but watching it will make your brain cells die faster.

Is My (Uri) Hubby Mr Oh counted as contract marriage? If yes, I loved this one. 💓💓💓 and this is my recommendation.

My Husband Mr Oh!

Full House and Sassy Girl Chunhyang - both of which had those elements- were my entries into kdramaland. I think there was a contract element to My Name is Kim Samsoon too, though her working at Jin-heon's restaurant would have meant they would have run into each other anyways.

Such a common trope in cdramas too.

A bit morally gray, but I enjoy its related trope - "you've forgotten because you have amnesia, but you're my husband/wife/gf/bf", a la 100 Days My Prince and Haeundae Lovers

Not really a contract relationship…but a forced one. Oldie but gold- Princess Hours

I just watched the Japanese Fight Song on Viki, and I really enjoyed it. The contract relationship happens because the FL wants to make memories before a looming surgery, and the ML needs to feel to write songs again. Possibly because I went through a health scare where for a while it looked like something similar was going to happen to me, I really felt this one. Amazing depiction of a non-typical family. Although the FL made some decisions at times that weren’t the best, they made sense to me as the only way she could deal with what was happening to her- coping is sometimes survival. The ending was very sweet, though. Not tons of kissing, lol, for anyone missing that old romance build up feeling.