Can't adopt the child I want

I have family who I wanted to adopt two children. When I sent them to the computer to adopt, there was a toddler and a child whom I really liked in the list of available children. I adopted the toddler, but when I went back to get the child, the list had changed. I've had them look at least ten times since and the child I want has not reappeared. Is there any way I can change the list or see more kids? I really want this one girl and I've had aging off in the game for weeks waiting on this kid, which is getting annoying with the toddler.