As Nick says, there's nothing in the api that will help you here, but you might be able to get what you want "manually". The "shape" of the custom report endpoint url is:
https://rally1.rallydev.com/slm/analytics/reports/<id>/run?PROJECT=<project oid>
where <id>
is the id of the report (which you can get by hovering over it in the Reports tab index) and <project id>
is the id of the project from which to gather data.
ex:
https://rally1.rallydev.com/slm/analytics/reports/1001883/run?PROJECT=20383843
(don't bother trying that as is, those are dummy ids). You'll still need to use the appropriate LoginKey.