Pregnancy dramas

All Japanese...

Pregnancy:

Gyne
Umareru
14-sai no Haha
Last Friends
11nin mo Iru!
Madonna Verde

Young children:

Edison no Haha
Aishiteru
Hikari to Tomo ni
Daisuki!!
Yoiko no Mikata
Mother

Dads and kids (including stepdads, etc.):

My Girl (Japanese)
37.5 C no Namida
At Home Dad
Hito ni Yasashiku
Papadol
Mama wa Idol
Shiroi Haru
Good Life
Kaseifu no Mita
Oh My Dad
Oh My Girl

Bad Couple

J-drama:

Virgin Road

It's an older drama and I know some people are hesitant to watch the older ones, but this is a really good one, imo. I loved it. I watched it because I, too, was searching for something about pregnancy (I'm going to check out some of the recommendations above), and I'm so glad I did.

It's about a young woman who gets pregnant by her older lover, but they break up before he finds out. She is going home to see her father and brother and doesn't know what to do, but on her way home she meets a guy who agrees to act as her fiancé, until she is ready to break the news to her family that she is going to raise the child on her own. That's the start of it. Admittedly this drama has some of the usual clichés (a father who thinks he always knows best, a super annoying second girl...), BUT it didn't bother me too much because I really liked the main couple and their road to happiness. I liked the male lead so much. I found it to be a cute and moving drama.

I also recommend Daisuki!!! 

You already have some great recomendations, but I'll leave mine as well (I'll list movies also):

Pregnancy at some point:
14 sai no haha (J)
Ai wa Mieru (J)
Umareru (J)
Only You (K) - similar to Autumn's Concerto
MoMo Love (T)
Summer Snow (J) - Not the main story
Daisuki! (J)
Jenny & Juno (K)
Dekichatta Kekkon (J)
Koizora (J)
The Princess' Man (K)
King2Hearts (K)
It Started with a Kiss (T)
Itazura na Kiss: Love in Tokyo (J)

About Raising Children:
Abarenbo Mama (J)
Celeb to Binbo Taro (J)
Le Jun Kai (C)
Mother (J)
Myu no Anyo Papa ni Ageru (J)
Baby & I (K)
Harmony (K)
Natsu no Koi wa Nijiiro ni Kagayaku (J)
The Moon That Embraces The Sun (K)

Also I don't know if you like historical chinese dramas, bur if you do, most of historical dramas set in Harens deal with pregnancy at some point, children and heirs:
Legend of Concubine Zhen Huan
The Virtuous Queen of Han
Legend of Lu Zhen
Desperate Love
Scarlet Heart - I don't recomend the second season though

Hi!! :) I hope you don't mind this pregnancy thing being associated with the crime genre...if so watch..
Two Weeks...It's a K-drama..http://mydramalist.com/7028-two-weeks
Nightfall...it's a HK movie...http://mydramalist.com/4299-nightfall
Last Friends...it's a J-drama (not a crime one...this has to do with life and friendship. The pregnancy thing happens towards the end)...http://mydramalist.com/1295-last-friends

JDRAMA
Dekichatta kekkon
My girl
Zenkai girl

TWDRAMA
Sunny happiness

KDRAMA
Wonderful life
Only you

Umareru
14-sai no Haha
Dekichatta Kekkon
Daisuki