EDIT: I think this is the COBOL Covboys discussion I referred to above: https://news.ycombinator.com/item?id=14083214
A lot of the big mainframe software companies like CA Technologies, Rocket Software, or BMC hire people with no mainframe experience (often straight out of college) and then train them.
If you're willing to pay for it, IBM offers classes in Dallas, TX for beginners as well. They are not cheap.
Marist College (located in New York, I think) also offers some z/OS certificates and classes. Unfortunately, I don't think they are online. I could be wrong about that though. http://idcp.marist.edu/enterprisesystemseducation/zosprogram...
It will literally take you months to do something in COBOL on the mainframe that would normally take you a week in anything else. Trust me, you take for granted all the conveniences of modern programming environments. COBOL is very much a product of it's time and it's time was decades ago. The success of these old environments rests entirely on extremely well defined (and tedious) processes, not the technology.
No matter how much they pay you, you probably still won't want to do it -- it's just not intellectually stimulating enough and you will constantly be frustrated.
Fixed that for you.
The environment is also terrible but separating COBOL from the environment is pointless.