Soft Touch - S2-E22
Visible crew/equipment: When Doug and Carrie go to get up from having dinner with Saskies, tape markers are visible on the floor by their chairs. (00:05:30)
Queasy Rider - S2-E1
Visible crew/equipment: When Doug and Carrie are arguing over the bike a white tape marker can be seen on the floor. (00:09:20)
Visible crew/equipment: In the opening scene, when Doug almost sits on Arthur, you can see part of the blue mat that Doug rolls Arthur off the couch on to.
Visible crew/equipment: When Doug is sitting in the living room and Carrie comes into the kitchen carrying groceries, a boom mic shadow is seen moving on the wall behind her. (00:04:10)
Visible crew/equipment: When Doug is talking on the phone, the shadow of a boom mic moves on the wall behind him. (00:00:20)
Dire Strayts - S2-E8
Visible crew/equipment: When Carrie storms out into the back yard, Doug follows. When he does, the kitchen door stays open and if you look at the glass it reflects all the stage equipment above the set in the kitchen. (00:07:00)
Visible crew/equipment: When Carrie walks in and sees Hollie for the first time in the episode, a boom mic can be seen following Carrie across the kitchen. (00:07:00)
Visible crew/equipment: When we see Arthur playing Shuttleboard for the first time, his mic pack is visible. (00:08:00)
Frozen Pop - S2-E15
Visible crew/equipment: When Doug goes to scrape the car, a stage light is reflected in the iced up windows. (00:01:05)
Visible crew/equipment: The second time Doug pulls up at the toll booth, stage lights and equipment are reflected in the car's paintwork. (00:07:20)
Visible crew/equipment: During the drag race at the end, several times on the van you can see camera shadows. (00:19:10)
Visible crew/equipment: When Doug is lying on the floor with the phone on him, the camera zooms in and you can see a boom arm reflected in the phone. (00:19:35)
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.