Frozen Pop - S2-E15
Visible crew/equipment: While Doug is scraping the windshield in the wide shots, the end of the street backdrop and production equipment are visible at the upper left side of the screen. (00:01:15)
Visible crew/equipment: Doug whisks Carrie to the boardwalk straight from the train after work, and when Doug points to the booth with plush frogs, a camera is visible on the left side of the screen as it moves out of shot. (00:17:20)
Visible crew/equipment: When Doug uses the ridiculous RV horn and startles Carrie awake, as she walks from the sofa to the front door, the overhead studio lights are visible at the top of the screen. (00:11:40)
Soft Touch - S2-E22
Visible crew/equipment: At the start, in the shots facing Carrie and Doug while they're in the car, we can see a screen atop the roof on the driver's side of the car with its reflection on the windshield (and its shadow on the car's hood). This is gone in the overhead long shots. (00:00:10)
Visible crew/equipment: Jessica asks Carrie what number they live at - as she does so a tape marker is visible on the floor. (00:06:50)
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: 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)
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)
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)
Party Favor - S2-E13
Visible crew/equipment: When Doug and Carrie are arguing about Danny coming over, you can see a stage light (not on) through the door window. We can also the neighbours garage, which we know from many outside shots of the Heffernan's backyard, is not that close to the house. (00:01:50)
Party Favor - S2-E13
Visible crew/equipment: When Doug goes back to the house after unsuccessfully scraping the frost off the car, a stage light is reflected in the window to the right of the front door. As Doug approaches the door his own shadow passes over this reflection. (00:01:30)
Frozen Pop - S2-E15
Visible crew/equipment: When Doug is scraping the car, watch carefully and you can the the reflection of someone off screen behind the camera move. (00:01:10)
Dire Strayts - S2-E8
Visible crew/equipment: When Carrie asks what Deborah is like, on the cupboard door above Doug you can see the reflection of a boom mic moving around. (00:04:45)
Dire Strayts - S2-E8
Visible crew/equipment: When Doug says about watching the game at his on the big screen, a boom mic drops into shot very quickly. (00:01:45)
Visible crew/equipment: When Carrie and Doug head out to the garage the first time, a boom mic is reflected in the door's glass. (00:04:05)
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.