I have a database with about 50 tables with use together about 1 GB space.
The SQLite database will be readonly.
This copying will be done once each month.
EDIT:
I see one possible solution using linked server via SQLite 3 ODBC Driver which results in rather simple t-sql scripts. I don't know about its performance.
I guess that other solution require more work, but obtain better performance.
Best Answer
I have successfully used SQL Server Integration Services (SSIS) to setup a job to "archive" data to SQLite databases. A quick way to build a SSIS job, is to do a Task->Export Data task. At the very end you will see a checkbox on the top left asking you if you want to save this as a SSIS job.
Make sure that you have installed the SQLite provider from http://sqlite.phxsoftware.com/
You can schedule this SSIS package once it is saved.