Continuity mistake: In the exterior shot of Coopers there is a car parked, no bins, no people. However, in the immediate interior shot, you can see a garbage bin, newspaper box and people walking by in either direction. (00:13:15)
Factual error: At Shea Stadium, in Queens New York, Carrie asks Arthur if he want a Coolicoo. Carrie then goes to the concession to buy Coolicoo's and tells the guy behind the counter she can see them next to him. However, Coolicoos don't exist at Shea Stadium. They are only available at Dodgers Stadium in L.A.
Revealing mistake: When Doug and the rest are at a ballgame, the man sitting behind them is eating a hot dog. Actually he's pretending to eat, it never shows any bite marks and the guy is pretending to chew it.
Continuity mistake: At the ball game right before Carrie gets to the front of the concession line, there is a woman right behind here followed by a man. When she gets to the front of the line, the extras behind her have switched.
Continuity mistake: When Ritchi and Spence are at the cafe, Spence pours the remainder of the pitcher into his cup. The shot goes back to him, and it appears he took a large sip because his cup is near empty. When Doug and Deacon come in, Spence's glass is almost full again.
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.