Consider editing you .htaccess file so that it will phrase .html files as php files. Then just add a block of code to the html files that you want the counter on. It might look like this:
<?php
include ("/path/to/counter.php");
?>
I should also note that when you do edit your .htaccess file to phrase .html files as php files, the server will still phrase the html in you files too, so any of your .html files that are all html and contain no php will still look the same.
I'll try to find the code you need to put in your .htaccess file to make your server phrase .html files as php files.