The film that you most likely saw was the 1994 direct to video "classic" American Cyborg: Steel Warrior
This is for several reasons including:
- The source novel for Children of Men was released in 1992, 2 years before American Cyborg: Steel Warrior was released on DVD. While the core narrative is the same (a world suffering from a depopulation crisis) the film and the novel diverge in narrative structure and characters. It's likely that either writer of film read the novel, or perhaps read a treatment of similar story that diverged just enough to avoid legal action from being taken.
- Both films and the 1992 novel have a similar core elements that match that of a 1964 novel called Greybeard, What is odd about the 1994 is that it is so close to the 1964 novel that legal action should have been considered if it wasn't undertaken. Either way, the core narrative (a single pregnant woman in a sterile world)
Anyway, the 1994 film was released direct to video and seems to have been a staple of late night cable fare (which is where I saw it in either 1996 or 1997) meaning that you would have ample opportunities to have viewed it. Again, while it has similar elements to Children of Men, the narratives diverge so widely beyond the core elements that they are actually different stories altogether by their endings.
Reference:
https://www.theguardian.com/books/2013/dec/13/brian-aldiss-science-fiction-author-review