Advice please

My friends cousin wants me to adopt her child,she had a affair with a african american man and the child is biracial my husband is white and I am african american. My husband and I have a 11 year old child and would love the opportunity to be a forever family for this child. I am confused about how a "private" adoption works,the childs birth father is listed on the birth certificate but has not seen the child since she gave birth,the child is three now. The birth mothers family will not accept this child and she is engaged to another man that is not willing to raise someone else's child. Ever since she asked me and my husband to consider adopting the child its all we can think about. I want to write her a letter and tell her more about us,she knows we wanted to adopt and basic things about us from reading my blogs and my myspace page,but i have not seen her in years. How do you write a please pick us letter? What is a safe way for both us and the mother to make this adoption happen? Any advice would be greatly appreciated.