I am aware this is an old question but my solution may assist others.
I find that the JSON(P) services which make this easy do not last forever but the following JavaScript works well for me at the time of writing.
<script type="text/javascript">function z (x){ document.getElementById('y').innerHTML=x.query }</script>
<script type='text/javascript' src='http://ip-api.com/json/zero.eu.org?callback=z'></script>
The above writes my server's IP on the page it is located but the script can be modified to find any IP by changing 'zero.eu.org' to another domain name. This can be seen in action on my page at: http://meon.zero.eu.org/