cp my_private_files* /path/to/private_directory
chown -R myuser:myuser /path/to/private_directory
chmod 700 /path/to/private_directory
But they would still be able to scp to their home directory (you can make home directories each a small disk partition, say 100k or so) and likely /tmp. You could disable swap /tmp also.
Keep in mind, if you did this, you couldn't sftp either.
You could remove this line from /etc/ssh/sshd_config
Subsystem sftp /usr/libexec/openssh/sftp-server
But even if you did this, I could still "cat somefile" to the stdout screen output
then copy and paste that output to my local computer.