Disabling logging on certain tables
Is it possible to disable logging on certain tables within the database?
  Can I place the two tables in the same schema, then disable logging on the schema?
  Is the only option to move the two tables to a separate database, and disable logging there?
  


Logging of user operations cannot be disabled.

There is a class of operations called minimally-logged operations that only allows a transaction to be rolled back (as opposed to also being able to roll forward). However, it doesn't sound like what you're doing would meet the criteria for that to apply, nor do I think this would solve the problem anyway.

The SQL Server solution would be to land the staging tables in a new database in SIMPLE recovery, separate from the aggregation results database, which I assume is in FULL recovery. While this wouldn't decrease the volume of logging, it would eliminate the need to back up the log generated by the data loads. (See my blog post here about logging, and some of the factors involved in choosing a database's recovery model.)

Separating the tables into another database would provide the flexibility to land the log file on a faster I/O subsystem, probably a small array of locally-attached solid-state drives.

Also, consider that SQL Server alone may not be the best solution to solve the problem. There are other RDBMS solutions that offer the ability to completely disable logging for certain tables. The data could be staged and aggregated in another system, and the results merged into the existing SQL Server database, which is well-protected by full logging and backups.