Deconstructing Carrie - S7-E15
Continuity mistake: In the kitchen when Arthur says he was a terrible father and gets up, Holly looks over at him with her hand on the edge of the table. She says, "Oh no", but then she's smiling. When the shot changes angle, her arms are crossed. Then Holly says, "Better than my dad, who was too busy chasing the almighty bottle of glue", her hand is instantly on the box of photos again. (00:11:35 - 00:12:05)
Silent Mite - S7-E7
Continuity mistake: In the final scene where Arthur raises his ornament on the Christmas tree, the kitchen door is closed behind him. In the next shot looking out from the kitchen, the door is already open as Arthur walks forward and through it. (00:21:15)
Silent Mite - S7-E7
Continuity mistake: In the final scene where Arthur takes his ornament from near the bottom of the tree and puts it closer to the top, the door to the kitchen is closed. Then in the next shot from inside the kitchen, the door is already open as Arthur walks towards camera. (00:21:15)
Deconstructing Carrie - S7-E15
Continuity mistake: Doug is sitting on the couch making club music sounds and moving his hands when Carrie reaches out and touches his face to make him stop; then his left hand is instantly on the arm rest. (00:13:10)
Deconstructing Carrie - S7-E15
Continuity mistake: While Carrie was being harassed by the construction workers, Doug was watching by looking out the door to the right. In the next shot, you see Carrie through the window, coming in from the left.
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.