Black ops actually needs just under 9gb to install, therefore your 2gb is what is restricting you.
30gb for steam, games and operating system is not going to give you any change.
My advise would be to stick steam and it's related content on the drive that has 930gb, you wont have to worry about disk space for steam games for quite a while.
To do that all you have to do is uninstall steam and install again but this time when it asks if you want a typical install or custom, you choose custom. You will then be given the option of installing to a directory of your choice, you choose 930gb drive.