Sorry, I only read your actual request now...

Korean dramas are extremely conservative. You're more likely to find a movie rather than a drama. And even a Kmovie featuring gay characters is a rare thing (and it would probably be gay men, not women).

There's a Thai movie called "Yes or No" that even has a sequel. It's all about the two girls in love. http://www.youtube.com/watch?v=WCYjf8zhGJ8

And look, I found a whole list of Japanese movies about it: http://www.listal.com/list/japanese-lesbian-film
Thank you, algelic! :)
Even though this topic is really old already, I'd add Majisuka Gakuen to this list, it has tons of subtext especially in season 2, season 3 even has an actual couple. It's a good J-Drama with lots of cool characters so it's worth checking it out.

There's also this korean movie called As One which, aswell, has a lot of subtext and the movie itself is great.
*jumping into old thread* Hormones 2 has a lesbian storyline, which will probably continue on into the next season (airing in summer 2015). Other Thai dramas like Room Alone also have some lesbian characters, but IMO the depiction is kind of side-eye worthy. But overall definitely don't rule out Thai dramas/movies if you want LGBTQ storylines/characters since there's a lot of it there
In Philippines there's a drama airing about Lesbian its called Rich Man Daughter.. :)
In the J-drama Piece, the main character's female classmate ends up confessing her love to her. It is one-sided but I thought that the way they dealt with the confession and Mizuho (the main character)'s reaction and acknowledgement of it was excellent. 

Slightly unrelated but I'm just finishing up Coffee Prince and, even though it isn't a gay relationship because Eun Chan is really a girl pretending to be a guy so she can work at Coffee Prince, the emotional turmoil and, finally, acceptance that Han Kyul experiences when he thinks that he is gay was very well presented. I also appreciated the other characters in the drama telling him that it didn't matter if Eun Chan was a guy, that it would still be fine. Han Kyul was prepared to be judged by society and his family but he didn't care because he loved Eun Chan.
I'd like to know this also, thus while checking out the other comments, I'll keep this in my posts.
Seonam high school investigators has 2 episodes based around a lesbian relationship it was also the first (and only as far as I know) Korean drama to show a lesbian kiss! Butunfortunately it was only a 2 episode focus.The overall series is really good though I recommend!
The show Mendol Ikemen has two girls that are into each other. Japanese.

As far as I know, Korean culture has a taboo around homosexuality so you won't see much from them.
Transit Girls started airing not too long ago and it's a J Drama about two young women falling in love and I LOVE it. It's extremely sweet and the story focuses only on them. It's short but totally worth it.
A new web drama just started called Lily Fever. I couldn't find much info on it, but watched it anyway. It's really cute. My only complaint is that it's not long enough. There's 3 episodes and a prologue out so far.

https://www.youtube.com/playlist?list=PLdBvEUNP7RyeLcb8WCKDnRjOxqTW00fun
At the moment Japanese drama transit girls the Japanese seem more liberal than the Koreans when it comes to homosexuality unfortunately...wish they were more accepting
It's not a Korean drama , it also a movie. A Thai movie. It was my first time watching a Thai movie or something Thai. It's a lesbian movie, it's really good. It's called "yes or no". You'll love it.
The Korean movie, A Bizarre Love Triangle, has a lesbian relationship, but that's the only one I can think of that hasn't already been mentioned. (idk if lesbian relationship is really accurate, I mean between just the two girls the relationship itself is lesbian but the orientations aren't strictly lesbian.)

Also if Painter of the Wind counts then Sungkyunkwan Scandal should fit too (If I remember correctly).