Well, this question is old but still has no answer!

Here is a small solution for future visitors.

Implementing load more button for comments without plugins is simple enough:

1. Create a button if comment pages are 2 and more
2. Create a jQuery script that will process the button click event and passes the current comment page number to wp_ajax_ action hook
3. The last step – is wp_ajax_ function that will process the AJAX request.

That’s all!

But if you need the ready code, please look at this tutorial https://rudrastyh.com/wordpress/load-more-comments.html