Is 'convert' in the path for the user the web server/php is running as?
I do it like this:
$image = "/path/to/image.jpg";
$new_height = "100";
$new_width = "100";
$command = "/path/to/convert -geometry " . $new_width . "x" . $new_height . " " . $image . " " . $image;
exec($command);
I'm guessing it is a path problem for you though.
-- Jason