Try this - change
imagecopymerge($image, $watermark, $dest_x, $dest_y, 0, 0, $watermark_x, $watermark_y, 100);
to use a slightly different function, and remove the final variable:
imagecopy($image, $watermark, $dest_x, $dest_y, 0, 0, $watermark_x, $watermark_y);