With some clever cheating, you can adopt that kid.
You'll need either Inge's Teleporter Shrub modified for recent EPs or the Summon and the Family Tree objects of the InSimenator.
As I have no idea where to find that teleporter shrub at the moment, here's what you do with with InSim: Using the Summon tool, find the child that you're looking for in one of the "families" listed. It will teleport the kid onto your lot. Now, using the Family Tree Adjuster, use the option to add the child to the household or just use the in-game cheat for the same purpose.
I think the trickiest part will be actually finding that kid, but it doesn't hurt anyone if you summon some unwanted sims.
