If the biologial father is not a threat to the child, are you sure that adoption is the way to go, if he is now willing to have a relationship with his daughter? Unfortunetly for some parents getting served with petition to adopt papers is the "kick in the butt" that they needed in order to be a good parent. However their is usually a honeymoon period of a lot of contact and promises, that quickly slows down and goes back to the old pattern.
Keep a contact log and a behavior log, you can find out about both by going to the
http://stepparent.adoptionblogs.com/ site where you will find articles that explain how. Building a case for a stepparent adoption is not always easy, perhaps you could try hitting him with a child support order if he wishes to now have contact, that may get him to consent to the adoption.