This is what I use for merging two images while respecting the alpha channel (formulas are taken from the wikipedia article on alpha compositing; they're not too pretty as I didn't really try to make them look so, but instead just work and make sense when checked out months from now), with a quirk - an additional parameter (that defaults to NULL to be ignored) to manually specify a "transparent" color, which won't be copied over from the source to the destination. In comparison to the other implementation here, only one pass over $src_im is done, but more calculations are performed:

<?php
function imagecopymerge_alpha($dst_im, $src_im, $dst_x, $dst_y, $src_x, $src_y, $src_w, $src_h, $pct, $trans = NULL)
{
  $dst_w = imagesx($dst_im);
  $dst_h = imagesy($dst_im);

  // bounds checking
  $src_x = max($src_x, 0);
  $src_y = max($src_y, 0);
  $dst_x = max($dst_x, 0);
  $dst_y = max($dst_y, 0);
  if ($dst_x + $src_w > $dst_w)
    $src_w = $dst_w - $dst_x;
  if ($dst_y + $src_h > $dst_h)
    $src_h = $dst_h - $dst_y;

  for($x_offset = 0; $x_offset < $src_w; $x_offset++)
    for($y_offset = 0; $y_offset < $src_h; $y_offset++)
    {
      // get source & dest color
      $srccolor = imagecolorsforindex($src_im, imagecolorat($src_im, $src_x + $x_offset, $src_y + $y_offset));
      $dstcolor = imagecolorsforindex($dst_im, imagecolorat($dst_im, $dst_x + $x_offset, $dst_y + $y_offset));

      // apply transparency
      if (is_null($trans) || ($srccolor !== $trans))
      {
        $src_a = $srccolor['alpha'] * $pct / 100;
        // blend
        $src_a = 127 - $src_a;
        $dst_a = 127 - $dstcolor['alpha'];
        $dst_r = ($srccolor['red'] * $src_a + $dstcolor['red'] * $dst_a * (127 - $src_a) / 127) / 127;
        $dst_g = ($srccolor['green'] * $src_a + $dstcolor['green'] * $dst_a * (127 - $src_a) / 127) / 127;
        $dst_b = ($srccolor['blue'] * $src_a + $dstcolor['blue'] * $dst_a * (127 - $src_a) / 127) / 127;
        $dst_a = 127 - ($src_a + $dst_a * (127 - $src_a) / 127);
        $color = imagecolorallocatealpha($dst_im, $dst_r, $dst_g, $dst_b, $dst_a);
        // paint
        if (!imagesetpixel($dst_im, $dst_x + $x_offset, $dst_y + $y_offset, $color))
          return false;
        imagecolordeallocate($dst_im, $color);
      }
    }
  return true;
}

// use it like this (identical to imagecopymerge)
function imagecopymerge_alpha($dst_im, $src_im, $dst_x, $dst_y, $src_x, $src_y, $src_w, $src_h, $pct)
// or this
function imagecopymerge_alpha($dst_im, $src_im, $dst_x, $dst_y, $src_x, $src_y, $src_w, $src_h, $pct, array('red' => 1, 'green' => 2, 'blue' => 3, 'alpha' =>4))
?>