Try using get_stylesheet_directory_uri() instead of bloginfo('template_directory').
This function will give you the path to the style.css of your currently activated theme (the child theme). From there you can navigate to all sub-folders in your child theme folder.
<button id="buy" type="submit"><img src="https://wordpress.stackexchange.com/questions/251648/<?php get_stylesheet_directory_uri(); ?>/img/Buy-Now-Button.jpg" border="0" width="160" height="47" title="" alt="Buy One" style="cursor:pointer;"></button>