To access HTML encoder tool, login to your AuthPro Account manager and go to this URL:
https://www.authpro.com/cgi-bin/manager.fcgi?action=encode2
Make sure "Include AuthPro decoder and styles" and "Edit in visual editor" options are switched on:
If you do not have an AuthPro account, you can sign up here.
You need to duplicate original page to keep copy of content you're going to encode. Open members only page you want to protect in Google Sites editor and in Pages menu open page's options and select "Duplicate page". Don't forget to hide this copied page from navigation menu.
Publish and open copy of members only page you have made in previous step. You can copy all or part of your members area page content in HTML editor window.
When you finish making copy of members content in AuthPro editor, you can encode it and copy protected content to be pasted on Google Sites.
Open original members only page in Google Sites editor and replace existing content with encoded one using 'HTML embed' tool.
If you want to display message to someone who enter your website without being logged in as active member you can use this code:
<div id='need_login' style='display:none; font-size:20px; text-align:center; color:red'> Please login to access this page! </div> <script> if (auth_res!='ok') document.getElementById('need_login').style.display='block'; </script>
Just add this code to encoded content you have embedded to your Google Sites at previous step (it will not work if added as separate embed). Feel free to customize it as you like (change text, color or font size).