I had one of my sims adopt a child. In the adoption panel, there were three infants and 9(?) children to choose from. After I chose one, I started noticing all the kids from the panel wandering about parks and neighborhoods. In the manage populations screen, there were now several single-parent families with all the adoptable children.
I didn't note if the adoption could be cancelled once in the adoption panel or not, but it probably could be, and hopefully without charging the $1000 for adoption. If it is possible to cancel the action, just browsing adoptable kids may solve lack of children problem in games. I haven't tested in other files yet.
Jess