So long as the two points are roughly N/S of each other, then the simple rule of one nm per minute of latitude totally works. But that's the only time it works, so it's an optimization of a specific case rather than a general solution to the question "Using map coordinates - Anyone know how to use them by manual calculation?" as the OP asked.
Personally, I favor the finger/thumb method - you know, finger on one coordinate and thumb on the other one in an EFB app which then tells you the bearing and distance. But the OP asked for the manual calculation :-)