You haven't said what sort of relationship you had with the deceased adoptive parent. (Were you relatives? or friends?)
Did the adoptive parent have a will naming you as guardian in the event of his or her death? If so, you should have no problem getting custody of the child. Otherwise, you will have no choice but to go through social services. In the meantime, it wouldn't hurt to check with an attorney, if you haven't already.
All the best.