Wordpress - How to override JavaScript files in child theme?

Child themes only override php files (like header.php) that are included 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.

Like so...

<?php
// hook in late to make sure the parent theme's registration 
// has fired so you can undo it. Otherwise the parent will simply
// enqueue its script anyway.
add_action('wp_enqueue_scripts', 'wpse26822_script_fix', 100);
function 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.