Some private agencies specialize in international, others infants and others in older children from foster care. You just have to do your research, Usually if you call one they know which agency does which and will refer.
There are no children in foster care with nothing wrong except a need to be with siblings. All kids in care are there because of neglect, abuse or abandonment. Some have more difficult histories but they all ahve a reason to be in care but that doesn’t mean they all have huge problems.