I Need Romance
I Need Romance 2
It's Ok It's Love (the romance starts pretty early)
Koizora
Kuzu no Honkai
The World That They Live In (they basically start off when they have broken up, but get back together pretty soon) (I think I remember right, it's been a long time since I have watched it)
Bubblegum (the couple starts off as best friends)
Cheese in the Trap (he asks her out in ep 3)
Goblin
The Time We Were Not In Love (again best friends)
Last Cinderella
Love O2O
Marriage Not Dating (well, they pretend to start dating, but everything is believable)
Nigeru wa Haji da ga Yaku ni Tatsu (We Married as a Job)