If you're on SQL2005 or above there's a SSRS SDK sample to do what you describe by extending rendering to include printing. You then use SSRS subscriptions to scheduled the report.
While SDK sample is "unsupported" I've used it twice with no issues. Allow about 2 days to install the SDK sample and get familiar with what it does (and what it doesn't as there are a few gotchas). Once done, its all pretty standard SSRS from there on.