Here is a diffcult one in the world of asian dramas lol, I would like to find some fluffy romance, the kind that gives you the feels, with little drama in regards of the leads relationship. I got this urge while watching weightlifting fairy Kim Bok Joo, and i guess that be a good example up unil now. That means the drama can be there in other aspects, but not be the main aspect of the relationship betweenthe leads, like OMG WILL WE EVER BE TOGETHER, EVERYONE TRIES TO BREAK US UP or similar variations. Someone give me a break from the suffering pleeease
Any country will do ^^
Shopping King Louie and Weightlifting Fairy Kim Bok Joo

W - is pretty fluffy, ppl don't really care about their relationship that much
Another Miss Oh - the romance issue in this is more like between the couple, but there is some "I want you guys to break up!!" scenes too but they're not that important :)
Shopping King Louise - probably the fluffiest romance K-drama out there without any relationship problems!
Good Morning Call
Cheese in the Trap
The memorandum of kyoko okitegami
Oh my ghost

http://mydramalist.com/14574-my-love-story
My Love Story!!

it's existence is romantically fluffy
Thai dramas take the cake when it comes to fluffy romances. 
Ugly ducling series - perfect match and dont
u prince series - the lovely geologist
Full house 
Totally agree with Kokodus and for "Full House" Thai version is the best.
Healer and Love O2O
I second Love O2O, just finished it and its lovely.  Really low on the angst.  They face any drama together as a team without either one doubting the other.   Boss and Me is cute too and a bit fluffy.  Go Ho's Starry Night was low on the drama high on the humor.  Quite cute.  I actually really do not do well with a lot of drama and angst...   
I also recommend full house thai version but honestly I think that one does have a lot of drama...I had a hard time with the last several episodes.  
Nigeru wa Haji da ga Yaku ni Tatsu

And I also second Shopping King Louis
Definitely agree with Shopping King Louie and Love O2O!

I also think Oh My Venus is super fluffy and no one is ever really against them being together

I'm 7 episodes in on My Mr. Mermaid, so far it's drama free. Also heard mother in law supports the relationship, and pretty much most of the characters on the show. There is an angst bromance between four friends, but it's not the focus, and the bromance between Qi Ruifeng and Yibai, makes up for it. I often have the same problem, but I love this one because it's so drama free and cute and innocent, but still meaningful. Agh. I love it

something about 1% the remake 

Whats Wrong With Secretary Kim: fits your description perfectly  even the ML's mother ship them