I believe you can do this to fix this problem:

[ProtoContract(SkipConstructor = true)]
public class Parent
{
    [ProtoMember(1)]
    protected List<Child> m_Children;

    private Parent() { Initialize(); }

    [ProtoBeforeDeserialization] // could also use OnDeserializing
    private void Initialize()
    {
        m_Children = new List<Child>();
    }

    public Parent(List<Child> children)
    {
        m_Children = children;
        m_Children.ForEach(x => x.Parent = this);
    }

}