On my local environment, the following settings work in my index.php file:

$system_path = '../../ci/system/';
$application_folder = '../../ci/application';

My folder structure looks like this:

-ci
---system
---application

-public_html
---site
----index.php

This works on my local environment, but when I upload my files, I get an error message:

Your system folder path does not appear to be set correctly. 
Please open the following file and correct this: index.php

I tried the following:

$system_path = dirname(__FILE__).'../../ci/system/';
$application_folder = dirname(__FILE__).'../../ci/application';