There are several reasons why this may be happening.
1. Glitch- the game is buggier than an anthill, so you may be experiencing a glitch in which you are unable to have children.
2. The number of children you can have may be influenced by the size of your house. I think the most children per household is two. Try buying a bigger house. If this is not possible...
3. Keep trying.
4. If your current child is still an infant, you will be unable to have another until it is grown a little older.
5. Also if someone is around you like your other kid or a villager while your in the bed room it wont work. You have to be alone in your house. To answer the general question you can only have two kids with one partner. You can adopt additional children or have children with someone else, if you want more after two.
6. Marry another person.
Here is an example of what can be accomplished