Alex,
There is no existing parameter, similar to $P & its supporting parameter $P, which can allow you to ask the user to input a specific user of the system, against whom the report should be run.
Also note that $P parameter represents the current user who has logged into the system and is running the report.
In your case, if you are using the source version of Centric, you can change the code and provide support for a new $P & $ parameters similar to $. The Parameter.java and ParameterList.java class have support for report parameters that need user prompts. You might have to add a new User selector pop-up if it does not exist already.
- Ananth