Board Thread:New on The Sims Freeplay Wiki/@comment-95.147.54.95-20140806192038/@comment-24468003-20140808034858

You have to get a crib in the Children's Store or in the Home Store under Infants. Put that crib in a house with a married couple and then click on crib and you can have a baby with Lifestyle Points. They take 24 hours to come.

If babies are still unavailable to you, you have to complete the Two and a Half Sims quest.