Private school blog is an ambiguous phrase that could mean many things.
A private school blog could be one that is kept and updated by the administration of a private school to share about events and changes in the school.
A private school blog could be one created by the administration and updated by a group of teachers, students, or parents to share information.
A private school blog could be one kept by a student for the purpose of sharing daily life in a private school and expressing personal opinions.
A private school blog could be any one of these.