SQL Server 2012 introduces contained databases ( http://msdn.microsoft.com/en-us/library/ff929071.aspx) - essentially these are databases which are somewhat isolated from the rest of the SQL Server instance.
By setting your database to partial containment you can created contained users - the credentials and privileges are stored in the actual database rather than in master and so a contained user authenticates against that database rather than the SQL Server instance. As a result if you are using database mirroring the login and permissions are automatically transferred to the mirror.
To create contained users you also need to set the sp_configure option 'contained database authentication' to 1 on both the principal and mirror ( http://msdn.microsoft.com/en-us/library/ff929237.aspx)
There are a few security best practices to follow to be sure your database stays secure - see http://msdn.microsoft.com/en-us/library/ff929055.aspx for more.
If you aren't using SQL 2012 then I realise this is not much use, but perhaps it's a good reason to upgrade!