Continuity mistake: When Doug is handing the deodorant back to Arthur the way he holds it changes between shots. (00:06:15)
Continuity mistake: When Doug Tells Carrie to pack for Atlantic City the cushion is either on or off her lap. (00:17:15)
Continuity mistake: When Arthur sits down to talk about the deodorant with Doug, Doug's hand is flat on the table. Camera changes and it's now on the doughnut box. (00:11:00)
Continuity mistake: At the start, Carrie is saying she wants popcorn with the movie and is motioning with 1 hand. Camera cuts and now both arms are outstretched. (00:00:30)
Answer: To answer the question directly. Carrie and Doug do not have a biological child during the show's main run. In season 3 or 4 finale (cant remember which) Carrie has a miscarriage. Later on in the show they find out Carrie has 1 working ovary. Thus reducing the chance of them conceiving. By the final season, they couple agree to adopt from China and go to collect their child in the show's final episode. While on the flight back from China it's revealed that Carrie is once again pregnant. However the last scene of the show is a flash forward showing that Carrie goes full term with that child and they are struggling with both kids.
Ssiscool ★
Adding on to this answer, I read somewhere that producers were afraid of the show having a "before baby" feeling and then an "after baby" feeling. Some fans feel that main characters, or the show in general, decline in quality after a major change. For example, Jesse and Rebecca on "Full House" after they had twin sons, and Daphne on "Frasier" after she married Niles.