It's not so hard to do by eye if you have good markings on the board and a decent stencil. I have done this myself countless times. Just make sure there's enough room nearby to look and see if you lined it up properly to match rows. I managed to be off by a row once and that was unfortunate.
OSH stencils sells cheap mylar stencils that work fine. And their instructions show how to do basically this. A BGA is a tough package to start on but it's definitely do able. Might be worth getting a cheaper socket or something to practice on first.
You don't need X-ray though, I used to think that too but it's really unnecessary. For a small prototype run at least. Definitely not for a student project.
Hope that helps. Your student will learn a lot doing this.
Jim