Child PPF Account - Yes, you can do that no problem in that you can also claim that in your IT return under 80C.

Take care of following things:
1) A Public Provident Fund (PPF) account can be opened by resident Indian Individuals and individuals on behalf of minors, not by NRIs.
2) Only one Public Provident Fund (PPF) account can be maintained by an Individual, except an account that is opened on behalf of a minor.
3) A Public Provident Fund (PPF) account can be opened either by the Mother or Father on behalf of their minor Son or Daughter; however the Mother and Father both cannot open Public Provident Fund (PPF) accounts on behalf of the same minor.
4) Grand-parents cannot open a Public Provident Fund (PPF) account on behalf of minor grandchild; however, in case of death of both the Father and Mother, Grandparents can open a Public Provident Fund (PPF) account as guardians of the Grand-child.