Many agencies when they conduct their referrals take this into account, even if you don't ask for it. Many people have said our son looks like my wife, and could have been his birth mother - blue eyes, blonde hair. We noticed this on the plane home where there were many couples that had adopted - an Italian couple had two small dark featured boys - a young mother had a curly blond daughter with blue eyes that was the spittin' image of her new mom. One of my best friends adopted from Guatemala - he is Hispanic, and she looks just like him.
My father was also adopted, and even though that was a long time ago, pictures of him compared to HIS father as a boy are astonishing.
You can make a choice this way if you are willing to adopt a child that has already been born (as strange as that sounds, most domestic adoptions that agencies conduct are arranged while the birth mother is still pregnant). They'll try to accomodate your wishes.
Adoption is NOT cheap, but depending on the route you go, and the financing - it can be affordable. For instance, Uncle Sam gives an adoption tax credit of 11,390 dollars for adoption. The state of Maryland gives a 5000 tax deduction. And several companies and government agencies have either adoption help or adoption grants, and some airlines and hotels will provide cut rates for adopting parents. There's a lot out there.