Continuity mistake: In the first shot inside Arthur's house, Carrie and Doug are standing together when Carrie mentions how tough it must be for Arthur. It then cuts to Arthur sitting at the table, with Doug right there sitting beside Arthur. Next shot Doug is still standing with Carrie as she urges Doug to spend some time with Arthur, so this is when Doug walks over to his father-in-law. (00:07:00)
Continuity mistake: When Sara is in the shower you can see in her shadow, creases from her swimsuit. (00:16:30)
Continuity mistake: The piano in the living room is ebony in the beginning of the episode. At the end of the episode the piano is brown.
Continuity mistake: At the start, when Carrie is talking to Arthur about being inseparable she has her jacket over her arm. Camera cuts and now she is putting it on instantly. (00:00:10)
Continuity mistake: When Doug talks about sleeping on his mitt, the way he holds it changes instantly. (00:00:45)
Continuity mistake: When Carrie says that Doug is losing brain cells in the garage due to fumes, the way she holds the tickets changes instantly. (00:12:20)
Continuity mistake: At the end, the shawl around Carrie's shoulder is either covering her shoulder or not depending on the shot. (00:20:50)
Continuity mistake: The door to the house is on a corner. However, in the interior shots, they have a window each side of the door.
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)
Continuity mistake: When Doug is handing the deodorant back to Arthur the way he holds it changes between shots. (00:06:15)
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.