Child themes only override files in the main theme directory (like header.php) that are called in with functions like get_template_part or get_header, etc.
The correct way to add scripts to WordPress is with wp_enqueue_script. If your parent theme uses this, you can override the JS files by using wp_dequeue_script and enqueuing your own.
add_action( 'wp_print_scripts', 'wpse26822_script_fix' );
wp_dequeue_script( 'parent_theme_script_handle' );
wp_enqueue_script( 'child_theme_script_handle', get_stylesheet_directory_uri() . '/scripts/yourjs.js', array( 'jquery' ) );
If the parent theme isn't using wp_enqueue_script, it's probably hooking into wp_head (or wp_footer) to echo out the scripts there. So you'd use remove_action to get rid of those functions echoing the scripts out, and then enqueue your own script.
If the script is hard coded into the template file, you'll just need to replace that template file in your child theme without the script tag.
If they used wp_enqueue_script calls that utilize get_stylesheet_directory_uri, then you shouldn't have to do anything. Since this isn't happening, you'll just have to poke around and see what the theme author did.