I am writing a class ptr_scope_manager to manage the creation and destruction of pointers in a given scope. I have studied the answers from this question:
Private constructor inhibits use of emplace[_back]() to avoid a move
And it appears that if I want to manage the creation of an object whose class has a private constructor, my internal std::vector can use push_back but not emplace_back to construct the object. This is because emplace_back uses an internal class to construct the object. That means friending the ptr_scope_manager is not sufficient to allow it to create objects with private constructors.
So what I have done is make two create methods, one for objects with public constructors and one for objects with private constructors that have friended the ptr_scope_manager.
template<typename Type>
class ptr_scope_manager
{
private:
    std::vector<Type> ptrs;
public:
    template<typename... Args>
    Type* create_private(Args... args)
    {
        ptrs.push_back(Type(args...));
        return &ptrs.back();
    }
    template<typename... Args>
    Type* create_public(Args... args)
    {
        ptrs.emplace_back(args...);
        return &ptrs.back();
    }
};
class public_ctor
{
    int i;
public:
    public_ctor(int i): i(i) {} // public
};
class private_ctor
{
    friend class ptr_scope_manager<private_ctor>;
    int i;
private:
    private_ctor(int i): i(i) {} // private
};
int main()
{
    ptr_scope_manager<public_ctor> public_manager;
    ptr_scope_manager<private_ctor> private_manager;
    public_manager.create_public(3);
    public_manager.create_private(3);
//  private_manager.create_public(3); // compile error
    private_manager.create_private(3);
}
My question is this:
Is there any way I can use SFINAE (or otherwise?) to automatically select between create_public() and create_private() based on whether or not the template Type parameter has a public or private constructor? Perhaps utilizing std::is_constructible?
It would be nice to have only one create() method that auto-selects the more efficient create_public() method where possible and falling back on the slightly less efficient create_private when necessary. 
Destructors and copy constructors cannot be templates. If a template constructor is declared which could be instantiated with the type signature of a copy constructor, the implicitly-declared copy constructor is used instead.
For normal code, you would use a class template when you want to create a class that is parameterised by a type, and a function template when you want to create a function that can operate on many different types.
What is the correct syntax of defining function template/template functions? Explanation: Starts with keyword template and then <class VAR>, then use VAR as type anywhere in the function below. 7.
There is no difference between using <typename T> OR <class T> ; i.e. it is a convention used by C++ programmers.
Live demo link.
#include <type_traits>
#include <utility>
#include <vector>
template <typename Type>
class ptr_scope_manager
{
private:
    std::vector<Type> ptrs;
public:
    template <typename T = Type, typename... Args>
    auto create(Args&&... args) -> typename std::enable_if<!std::is_constructible<T, Args...>::value, T*>::type
    {
        ptrs.push_back(T{ std::forward<Args>(args)... });
        return &ptrs.back();
    }
    template <typename T = Type, typename... Args>
    auto create(Args&&... args) -> typename std::enable_if<std::is_constructible<T, Args...>::value, T*>::type
    {
        ptrs.emplace_back(std::forward<Args>(args)...);
        return &ptrs.back();
    }
};
class public_ctor
{
    int i;
public:
    public_ctor(int i): i(i) {} // public
};
class private_ctor
{
    friend class ptr_scope_manager<private_ctor>;
    int i;
private:
    private_ctor(int i): i(i) {} // private
};
class non_friendly_private_ctor
{
    int i;
private:
    non_friendly_private_ctor(int i): i(i) {} // private
};
int main()
{
    ptr_scope_manager<public_ctor> public_manager;
    ptr_scope_manager<private_ctor> private_manager;
    ptr_scope_manager<non_friendly_private_ctor> non_friendly_private_manager;
    public_manager.create(3);
    private_manager.create(3);
    // non_friendly_private_manager.create(3);  raises error
}
                        I'm pretty new to SFINAE too, but I think it could be done something like
template<typename... Args>
typename std::enable_if<!std::is_constructible<Type, Args...>::value, Type>::type*
create(Args... args)
{
    ptrs.push_back(Type(args...));
    return &ptrs.back();
}
template<typename... Args>
typename std::enable_if<std::is_constructible<Type, Args...>::value, Type>::type*
create(Args... args)
{
    ptrs.emplace_back(args...);
    return &ptrs.back();
}
If Type is not constructible then the first variant will be selected, otherwise the second should be selected.
Note: This is not an answer to the title but to the intent of the author: ...That means friending the ptr_scope_manager is not sufficient to allow it to create objects with private constructors. ...and a proof of my statement in comment: wouldn't private custom allocator calling private (static) methods of the manager solve the problem without the need for SFINAE? That would allow the emplace to work.
IdeOne demo here
#include <deque>
#include <memory>
#include <iostream>
template<class T> class manager {
    static void construct(T* p, const T& val) {
        new((void*)p) T(val); }
    template<class U, class... Args>
      static void construct(U* p, Args&&... args) {
        new((void*)p) T(std::forward<Args>(args)...); }
    class allocator: public std::allocator<T> {
    public:
        void construct(T* p, const T& val) {
            manager::construct(p, val); }
        template<class U, class... Args>
          void construct(U* p, Args&&... args) {
              manager::construct(p, std::forward<Args>(args)...); }
    //needed for deque ...dunno why it is using rebind for T
        template<class U> struct rebind {
            typedef typename std::conditional<
              std::is_same<T,U>::value, allocator,
              std::allocator<U>>::type other; };
    };
    std::deque<T, allocator> storage; //deque preserves pointers
public:
    template<class... Args>
      T* create(Args&&... args) {
        storage.emplace_back(std::forward<Args>(args)...);
        return &storage.back();
    }
};
class special {
    friend class manager<special>;
    int i;
    special(int i): i(i) {}
public:
    int get() const { return i; }
};
int main() {
    manager<special> m;
    special* p = m.create(123);
    std::cout << p->get() << std::endl;
}
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