I was bored and started looking around in the Lessons menu. I clicked on the pregnancy lesson, and at the end it stated "Your Sim will receive a Birth Certificate that you can place on the wall!" I...
I think it goes to your sim's inventory but you can always showhiddenobjects and buy them yourself to make up for any you don't have. I wish having a baby at home still gave one personally... Going to the hospital is a bit buggy at times. My sim stands at the counter for an eternity then is taken back after Im sure the baby is already falling out between her legs. (That's how long it takes)
Mostly I have mine at home so... cheating them in is an option.