Set the -fill option on the point primitives.

#!/usr/bin/perl
use Image::Magick;

my ($col, $img_width, $row, $img_height);
# Create a new image

my $im = Image::Magick->new(size => '400x300');

# Give it a white background

$im->Read('xc:white');


# Put a rectangle in there somewhere
$im->Draw(primitive => 'rectangle',
          points    => '0,129 199,169',
          fill      => 'blue',
          stroke    => 'blue');


for($col = 50; $col < 100; $col ++ ) {
    for ($row = 150; $row < 200; $row ++ ) {
        $im->Draw(
         primitive => 'point',
         points    => "$col,$row",
         stroke    => 'white',
         fill => 'white'   # you missed this fill right here!!!!!!!!!!
+!
         );
    
    }
}

$im->Write("$0.png");
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