The following code will add TinyMCE to excerpt(s) on posts (or custom post types), make sure to follow the comments in the code for detailed instructions. This has been tested and works with WordPress 3.9+

Please let me know if you know of a better way to accomplish this!

function lb_editor_remove_meta_box() {
    global $post_type;
/**
 *  Check to see if the global $post_type variable exists
 *  and then check to see if the current post_type supports
 *  excerpts. If so, remove the default excerpt meta box
 *  provided by the WordPress core. If you would like to only
 *  change the excerpt meta box for certain post types replace
 *  $post_type with the post_type identifier.
 */
    if (isset($post_type) && post_type_supports($post_type, 'excerpt')){
        remove_meta_box('postexcerpt', $post_type, 'normal');
    } 
}
add_action('admin_menu', 'lb_editor_remove_meta_box');
 
function lb_editor_add_custom_meta_box() {
    global $post_type;
    /**
     *  Again, check to see if the global $post_type variable
     *  exists and then if the current post_type supports excerpts.
     *  If so, add the new custom excerpt meta box. If you would
     *  like to only change the excerpt meta box for certain post
     *  types replace $post_type with the post_type identifier.
     */
    if (isset($post_type) && post_type_supports($post_type, 'excerpt')){
        add_meta_box('postexcerpt', __('Excerpt'), 'lb_editor_custom_post_excerpt_meta_box', $post_type, 'normal', 'high');
    }
}
add_action( 'add_meta_boxes', 'lb_editor_add_custom_meta_box' );
 
function lb_editor_custom_post_excerpt_meta_box( $post ) {

    /**
     *  Adjust the settings for the new wp_editor. For all
     *  available settings view the wp_editor reference
     *  http://codex.wordpress.org/Function_Reference/wp_editor
     */
    $settings = array( 'textarea_rows' => '12', 'quicktags' => false, 'tinymce' => true);

    /**
     *  Create the new meta box editor and decode the current
     *  post_excerpt value so the TinyMCE editor can display
     *  the content as it is styled.
     */
    wp_editor(html_entity_decode(stripcslashes($post->post_excerpt)), 'excerpt', $settings);
 
    // The meta box description - adjust as necessary
    echo '<p><em>Excerpts are optional, hand-crafted, summaries of your content.</em></p>';
}