you must ungroup the svg (e.g. inkscape), so that you can select the countries individually. Then I hope your code will work. 

Actually, the whole SVG inside a g (group) tag, with a transformation.

1. <g transform="matrix(1.594335,0,0,1.594335,-1721.783,-693.262)">

But the isolated shape doesn't have this transformation, so is drawn outside of the sketch's area.
You have to apply the same transformation to see it in place:

1. PShape africa;
2. PShape country;
3.  
4. void setup() {
5.   size( 1000, 1000 );
6.   africa = loadShape( "BlankMap-Africa.svg" );
7.   smooth();
8.   noLoop();
9. }
10.  
11. void draw() {
12.   background( 255 );
13.   africa.disableStyle();
14.   fill(128, 255, 200); stroke(0);
15.   shape( africa, 0, 0 );
16.   setCountryColour();
17. //  saveFrame( "africa_population.png" );
18. }
19.  
20. void setCountryColour() {
21.   country = africa.getChild( "dz" );
22.   if (country == null ) {
23.     println( "no country found" );
24.   }
25.   else {
26.     println( "country found ");
27.     ((PShapeSVG) country).print();
28.   }
29.   country.disableStyle();
30.   fill( 0, 0, 255 );
31.   noStroke();
32.   translate(-1721.783, -693.262);
33.   scale(1.594335, 1.594335);
34.   shape( country, 0, 0 );
35. }

I think you can give inkscape a chance, it is free and opensource and I have good expierences with working on maps (size scaling, transformations, coloring etc.)