print IMG $graph1->png; should be
print IMG $gd->png;

You didn't provide any data so I made some up to get a working program :-

#!/usr/bin/perl
use strict;
use warnings;
use GD::Graph::lines;
use GD::Graph::colour;
GD::Graph::lines->import();
GD::Graph::colour->import(qw(:colours :lists :files :convert));

my @graph_R1 = ([1..50],
                [1..50],
                [11..60],
                [21..70]);

my $graph1 = GD::Graph::lines->new(800,600);
add_colour(nice_blue => [31,120,180]);
$graph1->set(
  x_label              => 'position (bp)',
  y1_label             => '% methylation',
  y2_label             => '# methylation calls',
  title                => 'Mbias plot Read 1',
  line_width           => 2,
  x_max_value          => 125,
  x_min_value          => 0,
  y_tick_number        => 10,
  y_label_skip         => 2,
  y1_max_value         => 100,
  y1_min_value         => 0,
  y_label_skip         => 2,
  y2_min_value         => 0,
  x_label_skip         => 5,
  x_label_position     => 0.5,
  x_tick_offset        => -1,
  bgclr                => 'white',
  transparent          => 0,
  two_axes             => 1,
  use_axis             => [1,1,1,2,2,2],
  legend_placement     => 'RC',
  legend_spacing       => 6,
  legend_marker_width  => 24,
  legend_marker_height => 18,
  dclrs              => [ qw(nice_blue) ],
)or die $graph1->error;

$graph1->set_legend('CpG methylation');
my $gd = $graph1->plot(\@graph_R1) or die $graph1->error;

open(IMG, '>','test.png') or die $!;
binmode IMG;
print IMG $gd->png;
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