How to initialize a private static const map in C++?

The C++11 standard introduced uniform initialization which makes this much simpler if your compiler supports it:

//myClass.hpp
class myClass {
  private:
    static map<int,int> myMap;
};

//myClass.cpp
map<int,int> myClass::myMap = {
   {1, 2},
   {3, 4},
   {5, 6}
};

See also this section from Professional C++, on unordered_maps.