And sadly, even if there were such a facility, you'd probably be viewed as a potential paedophile and have to undergo a Criminal Records Bureau check.
I don't know whether home for Children like Dr. Barnados have a system whereby you can befriend a particular child and take an interest in them. The whole business of befriending children these days has become so horribly fraught because of child protection legislation that even legitimate volunteers who work with children are giving up.