Qualifications
First off, you'll need to be good at math and science—if you struggle with basic algebra and geometry, this probably isn't the job for you.
You'll need to have an engineering background—with an emphasis in mechanical, structural, or the electrical kind.
Drafting experience is also a plus, along with the ability to read blueprints.
This means going to a college that has a good engineering program and getting at least a BA in Mechanical Engineering. You could do worse than finding yourself at MIT, Cal Tech, Stanford, or Harvey Mudd, just to name a few choices.
You'll also need to be a whiz on the computer—and not just when it comes to playing Roller Coaster Tycoon.
Computer drafting software like AutoCAD and 3D CAD is used for the design, and then proprietary software that determines things like G-forces and other roller coaster physics takes over.
Computer technology is also used to keep the ride running smoothly and to control all the safety features.
You'll need experience. Yeah, we know, it's sorta' like a Catch-22. You're looking for a job to get experience, but they won't hire you unless you already have it. That's what they make summer internships for.
There are very few companies that make coasters, so they hire those with the most experience. If you can't get actual experience building coasters, boast about your skills putting together other machines. This is a hands-on job.