If you are using a recent version of Coveo for Sitecore you may be able to change some config values by using the Coveo Command-Center. For other config values such as the SearchAPI URL, you will need to update the config file directly.
Most of the configurations you want to change will be under
If you are trying to bring the configurations you have from one environment to another, just make sure you are copying every Coveo config file under both App_Config/Include/Coveo and App_Config/Modules/Coveo folders.
Among all Coveo configuration values, there is one that is more sensible when doing this. I'm talking about the
<sitecorePassword> you can find in the
Coveo.SearchProvider.Custom.config file. This value is stored encrypted and the encryption key is not in any configuration file.
That's why besides copying the config files you should also make sure you have the
ENCRYPTIONKEYS if not using SC 9.x) entry on your
core database (or
WEB_ENCRYPTIONKEYS in the
web if you don't have core as part of your setup).