You have a couple of options. Probably the easiest will be to create a "dummy" logon to CE that your web application will use to get the report instance.
A couple of pieces of information about how CE works with reports....
There are report "templates" and report "instances" - both of which have a .rpt file extension. A template is the report with no data. This is what is run inside CE when a report is scheduled or viewed on demand. An instance is the result of a scheduled report being run; it contains all of the information in the template as well as the data from the scheduled run.
From what you've said above, I think you need to be able to find a specific instance[/] of the report to show the user. It sounds like you're showing the report template.
I haven't worked specifically in CE9 - we use BO XI - but there is an SDK available to help you locate the specific instance of the report that your user wants.
-Dell