Add to search posts query array with post IDS which will appear first

It is not the most elegant solution, but you could sort the results on your search page:

At the top of your page, make the wp_query variable available

global $wp_query;

Later in you code, if there are some results :

if ( have_posts() ) { 

  //your desired order
  $order = array(45, 78, 94);

  // a comparison function to sort the post array with your custom one
  function sortByIds($a, $b){
     global $order;
     $a = array_search($a->ID, $order);
     $b = array_search($b->ID, $order);
     return $a - $b;
  }       

  //we use usort to sort the wp_query post using a comparison function
  // note, we could use a closure if your php version supports it
  usort($wp_query->posts,'sortByIds');

  //then your normal code....
}

It is not an sql solution but it works.