Can deferred mahr be conditional on the birth of children?

If you wanted to you could completely do that.

All of these things are per negotiation, as long as they are not negating the objectives of marriage then they're per negotiation.

So if a woman says I'm not going to have children for you unless you give me X, Y, Z, this is not allowed.

But if she said, if I have a child for you, then X, Y, Z would be given as a gift. That's allowed.

If a man said to his wife I am not going to give you a mahr until five years pass. This would not be allowed.

Mahr has to be named at the time.

But if he says, if you marry me, I won't be able to pay mahr until five years later, but it will be a right that you have over me. That's allowed.

If he said, if you stay with me for five years, Then I will pay you double all of that is per negotiation and that would need to be codified in a clear agreement.

Too many times people are doing these things verbally and it becomes he said, she said.