EDIT

Forget my answer below. You could simply use wp_register_style and wp_enqueue_style described in this answer.

You could do it with an additional query variable.

1. Add a new variable to the $query_vars array with the query_vars filter

2. On the template_redirect action, make sure your custom.php-css file is included, if the query variable is set.

   // functions.php
   function wpse26013_add_query_vars(query_vars) {
       $query_vars[] = 'style';
       return $query_vars;
   }
   add_filter('query_vars', 'wpse26013_add_query_vars');
   
   function wpse26013_include_custom_css() {
       $style = get_query_var('style');
   
       if($style == 'custom') {
           include_once(get_stylesheet_directory_uri() . '/css/custom.php');
           return;
       }
   }
   add_action('template_redirect', 'wpse26013_include_custom_css');
   

Then you can add a simple css include in your header file.

// header.php
<link rel="stylesheet" type="text/css" media="all" href="https://wordpress.stackexchange.com/questions/26013/<?php bloginfo("stylesheet_url') . '/css/?style=custom'; ?>" />

Last but not least, you have to define your custom css file.

// custom.php
<?php
header('Content-type: text/css');
header("Cache-Control: must-revalidate");
header('Expires: ' . gmdate('D, d M Y H:i:s', time() + 1209600) . ' GMT');

$options = get_option('webeo');
?>
#header #logo {
    background: url('<?php echo get_stylesheet_directory_uri() . '/images/' . $options['header']['site_logo']; ?>') no-repeat;
}

You could also get the contents from the css file with the builtin PHP function file_get_contents() and print the css directly to the sourcecode.