Just added the television show 'Dallas' to the list of shows with a Barren Babe. The first year of the show focused on the characters of Sue-Ellen and JR and their 'lack of children' after 7 years of marriage. I rewatched the first three years of the show a few years ago on the Soap Network and was surprised by that storyline.
Another 'Dallas' character with fertility issues was Pam who suffered from a couple of miscarriages. But then -- and I can't remember the specifics -- she was either told that she could not carry a baby to term, and/or she was the carrier of a genetic disease.
If you do happen to catch these episodes from the 70s, please note the way that infertility is portrayed as a type of 'hysteria' that affects the mental health of the 'afflicted' character. I wonder if this was really how society viewed the plight of Barren Babes just 30 years ago.