What can I do to atone for my sin after accidentally causing the death of a child in a traffic accident years ago, especially since the child's family has forgiven me and refused the blood money (diyya)?

If accidental killing occurs before puberty, there is no sin on the killer, and the blood money (diyyah) is incumbent upon the 'Aqilah (male relatives on the father's side). If the heirs waive the blood money, the 'Aqilah are absolved. As for the obligation of expiation (kaffarah), the majority of scholars deem it obligatory (and this is the ruling given in fatwas and is the more cautious approach), while Abu Hanifa does not obligate it. The expiation is freeing a believing slave; if none is found, then fasting for two consecutive months.