Make sure you read the Postulates section first! Other ground work includes motives and divided which help us realize that there are good machines that want to keep humanity alive. There are bad machines that really don't. The compromised and ended up with a zoo.

Sperm/egg or at least actual DNA is crossed to form the children so that Residual Self Images match the parents both in appearance and genetic issues. Attempting to program all traits in by scratch rapidly approaches a level of complexity where it's just plain easier to use the actual parents to create the child. Given that the machines have complete access to the bodies of both parents, it seems reasonable to use their material.

How does everything else work? The idea that the machines have specific knowledge of everyone's knowledge and maintains and alters that is too daunting (although several comics on the website make that suggestion... but it's almost always a single key individual) and too much effort for something that can be easily automated. So here's our model:

The Process

1. The Matrix is a robust self-running simulation, so there isn't some sentient machine watching each and every copulating couple to decide whether they have children or not... they have virtual bodies which include virtual sperm and eggs which follow after reality.

2. If virtual conception occurs a flag goes up in the system to automatically begin creating a zygote from the two... information from that zygote is fed back into the Matrix (if that zygote was removed and examined in the Matrix it would be exactly the same one in reality).

3. Along with that the pregnancy code in the woman's construct is activated. This is an automated program based off the woman's real physicality (where stretch marks may appear, etc) but may or may not be exactly like her in real life, but it doesn't really matter for the sake of the illusion. This program includes morning sickness, etc. All with a realtime residual image construct of the actual fetus/baby being grown (remotely)... no mental connection yet.

4. Meanwhile, the baby is being grown in real life, plugs are added, the liquified dead is fed, etc.

5. For the first- say- 5 months the consciousness inside the woman's construct is a low-level AI, like that of a cat. All that's necessary is for the baby's construct to behave like a baby for the sake of illusion. However, once the baby has it's plugs in real life....

6. The baby in the woman's stomach for all intents and purposes is the actual baby (both construct AND consciousness). If it kicks in the tummy, it's because the baby thinks it's kicking... the illusion of the Matrix first begins in the womb. So you sing it Mozart and love songs or fight abusively all the time, etc. it actually affects the real baby's mental state once it's born in the Matrix. Just like the real world.

Everything above is based on biology/physics so it can be automated with no need for sentient intervention or decision making. It is consistent with the postulates we've put forth and the rest of the theory. It also consistent with the "Morning Sickness" comic allowing babies to be removed from a stalk without dying from being unplugged without a pill.