I think children would require the game to work on a time scale it just isn't designed for. Having a short pregnancy or childhood would seem to me to clash with being in the same game where going from one town to another can take almost a day. Just having the game skip ahead to the child's birth would cause a lot of problems. A lot could happen in a year, territory will change hands, politics will change, kings would want something from their vassals, and your character wouldn't be there for any of that. Plus, what would your army do during that time, take a paid vacation? Not to mention after 757 days your character can start losing stats, and a child would take a big chunk of that time.
I can think of a few practical ways children can be implemented, but none with much depth. If your character is male, you could impregnate your wife, after which you would get a relation bonus with certain lords for being a family man. If your game somehow goes on for 9 months after that and you still haven't lead your faction to conquering all of Calradia, the child would be born but that would have no other effect than your wife holding a baby when you visit her. Other than having an effect on your score when you retire, it shouldn't do much. You're simply too busy with war stuff to be a good, attentive father, you jerk. I think there's just no good way to handle female players getting pregnant. I would say that after you've been pregnant for a while you would no longer be able to participate in combat, but that would mean you would spend a lot of time not being able to fight. You could get around that by being able to appoint a companion as commander and controlling them in combat instead of your own character, a feature I'd like to see regardless of children being in the game, but still you would be doing that for a long time. And of course you could avoid all this by making children be born and grow up really quickly, but that wouldn't match with the tone of the rest of the game. Even if pregnancy was shortened to something that was still a reasonable amount of time, like two months, it wouldn't do much for my suspension of disbelief. I just don't think it would work in a game where time is thought of in days instead of months. I also thought of the ability to adopt an older child, maybe from a lord who has a very high relation with you, but that wouldn't be different enough from recruiting a companion.
Like imgran though, I would like to see children for NPCs. Not just random ones with no background to fill the numbers, but children of already existing characters. It would be cool for them to come of age after a while, then they become vassals of the same faction as their fathers, carrying the same banner and having the same name with a "II" after it. If you have a good relation with one of their parents they'll mention how their father or mother speaks highly of you and start with a high relation with you. They would be highly influenced by their father, they would be inclined to try to stick close to him, vote for the same person as marshal or recipient of a fief, join him if he defects to another faction, and so on. Or maybe they could be rebellious teens and always do the opposite.