C++ syntax for explicit specialization of a template function in a template class?

You can't specialize a member function without explicitly specializing the containing class.
What you can do however is forward calls to a member function of a partially specialized type:

template<class T, class Tag>
struct helper {
    static void f(T);   
};

template<class T>
struct helper<T, tag1> {
    static void f(T) {}
};

template<class T>
struct C {
    // ...
    template<class Tag>
    void foo(T t) {
        helper<T, Tag>::f(t);
    }
};

GCC is in the clear, here. MSVC has a non-standard extension that allows in-class specialization. The standard, however, says:

14.7.3.2:
2. An explicit specialization shall be declared in the namespace of which the template is a member, or, for member templates, in the namespace of which the enclosing class or enclosing class template is a member. An explicit specialization of a member function, member class or static data member of a class template shall be declared in the namespace of which the class template is a member.

Additionally, you can't partially specialize a function. (Though I'm unsure about the details in your case, that would be the final blow.)

You could do this:

#include <iostream>

struct true_type {};
struct false_type {};

template <typename T, typename U>
struct is_same : false_type
{
    static const bool value = false;
};

template <typename T>
struct is_same<T, T> : true_type
{
    static const bool value = true;
};

struct tag1 {};
struct tag2 {};

template< typename T >
struct C
{
    typedef T t_type;

    template< typename Tag >
    void foo( t_type pX)
    {
        foo_detail( pX, is_same<Tag, tag1>() );
    }

private:
    void foo_detail( t_type, const true_type& )
    {
        std::cout << "In tag1 version." << std::endl;
    }
    void foo_detail( t_type, const false_type& )
    {
        std::cout << "In not tag1 version." << std::endl;
    }
};

int main(void)
{
    C<int> c;
    c.foo<tag1>(int());
    c.foo<tag2>(int());
    c.foo<double>(int());
}

Though this is somewhat ugly.