want to watch dramas feauring either single father or single mother falling in  love

note the single father/mother doesn't have to be main character can also be side character

also doesn't have to be father but can be guardian like Cheer Up Mr Kim 

Marriage Contract
Ms. Temper and Nam Jung Gi 
One More Happy Ending 
Male leads are single fathers:
Oh! My Lady - Main plot element. The male lead is a famous actor and finds himself with a daughter he didn't know existed. Female lead helps him come to terms with it (you guess the outcome). Not an outstanding drama, but it fits what you're looking for, romance takes the back seat and the male lead growing up is the key point.
Ms. Temper & Nam Jung Gi - A good side part of the story, the male lead's son is really great on his own and his scenes with the female lead are the best. I highly recommend this one, hang on through the first episode, it can be a bit disconcerting... 
City Hall - really just a side element, but there are a few cute scenes.

For single mothers, I'll second Panda, Please come back, Mister is very good, not quite as straight forward in the "single mother" part, but one the female main is divorced (the father is another male main - the bad guy), and I guess you can count another female main as a widow raising her daughter (even if the main male lead is actually the father but no one knows it). I'm pretty sure my explanations aren't making sense but the drama is difficult to sum up, complex, but really good.
Love and Secret - The main girl gets knocked up by the main villain and she falls in love with the main guy.
Please come back mister - thumbs up. I still giggle at one particular scene ... i had to watch the behind the scenes for it all well. Great drama. Loads of LOL moments and very touching. Some good bromance between the male leads too.

A long long drama to watch is Sweet Sweet Bodyguard. It's single father second characer but although its long it does go quickly. I enjoyed it for the most part.

A slightly different concept to what your after but gives the same feeling - Down with love: He looks for a nanny to help with his nephew/niece.
Zenkai Girl - the female lead babysits her boss' daughter and the male lead is a single dad :)
Marriage contract
Zenkai girl
Bara no nai Hanaya
One more happy ending
Celeb to binbo taro
Couple or Trouble
Boku to Star no 99 Nichi
Easy Fortune Happy Life
Good Morning Shanghai
Down With Love
You will definitely enjoy Five Children, don't be discouraged for the amount of chapters. Believe me I start to skip a lot for most of the dragging dramas. This One was so entertaining that I enjoyed every single chapter. Give it a try it will not disappoint you in the least bit.