Hi,
How did you configure it ? Could you provide a screenshot of the settings of the shipping method ?
Also, are you logged in with a shipping address selected on the checkout before looking at the shipping methods selection ?
Since Correios needs the shipping address to calculate the cost, it won't display if you are not logged in.
Also, you need to have a weight and dimensions in your products. Did you do that ?
Finally, if you have other shipping methods, you can disable them and leave only this one enabled. If no shipping method is found on the checkout, it will display the error messages coming from the enabled shipping methods if any.