There are some really nice dramas that involve couples and children so I would definitely recommend you:
1. Wonderful life: it's one of the cutest dramas I've seen and it's about marriage and child
http://mydramalist.com/korean-drama/321/wonderful-life
2. Prime Minister and I - marriage and children ( maybe not exactly what you're looking for) but I highly recommend it;))
http://mydramalist.com/korean-drama/8129/the-prime-minister-and-i
3. Autumn's concerto - It's not k-drama, but it's one of the most amazing and heart warming taiwanese dramas I've ever seen so it's worth giving it a try
http://mydramalist.com/taiwanese-drama/81/autumns-concerto
Playful Kiss! :) They get married toward the end, but then there is another cluster of "after" episodes on Youtube that go through their married life. She gets preggers, and it's super cute. This is the Korean Drama version of Itazura No Kiss.
i just finished watching A Thousand Day's Promise. the main couple gets married and has a child with a lot of adversity in their relationship.
I can only think of Autumns Concerto which is one of my top 5 all time favorite
Queen of Reversals is exactly what you're looking for. It's an exploration of a marriage. They get married pretty early into it and have a child together.
This is a hard one, maybe wonderful days? They do get married and have a baby, but in the wrong order... And you also have Playfull kiss, but no children. Good luck
Love Now (goes romantically) Empress Ki (goes not romantically)
King2Hearts
and
Playful Kiss
2 of my all time favorites
Loving You A Thousand Times..
The lead couple married in the middle of the story and there is also a child involved. You can check it out. It's also a great drama.
Wonderful life

And if I remember correctly in 1% of anything fits the criteria.

You can try "tomorrow with you". They don't have kids in the drama but they get married by the fourth episode. It isn't one of my favorites but it's a good one. ^^

Smile, you fits this perfectly. Its around 50 episodes and it is very family-oriented.