As far as I know there is no way with SQL Server to keep the database online while it’s restoring. Restores are a point in time version of the database and without having exclusive access to perform the restore it can’t guarantee the state of the data if data was to get changed mid restore.
In the case of oops deletes and not a corrupted database. If you have the space to do a full restore you can restore the needed database with a different name and file name(s) which will allow you to query the needed data and reinsert or update the live database.
There is a product called LiteSpeed from Quest that I use (not connected to them) to perform backups and compression that will allow you to read the backup files without having to do a real restore. You will then be able to query the tables in the backup and store the results into temp tables in another database on the server. This option requires that you have backed up your database with the software so some advanced DR planning is required.
