As it stands, there aren't too many things that you will do in a "normal" Armour Corps career that will give you civilian qualifications. Of course, there are people who get specialty courses, depending on your job/position requirements. A few examples: First Aid Instructor, HAZMAT, Accident Investigator, Suicide Prevention, Alcohol and Drug counselor, Safety Management. You won't start getting those until the Cpl level (and senior Cpl usually), and then MCpl and up.
You can ask for courses, but avoid asking for courses that have nothing to do with your job, as it tends to annoy people. If you take training outside of the military (computer training, university/college courses) make sure you let your supervisor know, so it can get put into your file, and it can help you advance, career wise. As well, you may even get re-imbursed for the cost of the course (assuming you pass, and it is an accredited school).
One thing I will warn you about: watch out for the courses that nobody wants: it's usually for a reason. There are some courses/qualifications that are thankless jobs, and unless you really enjoy them, once you are qualified, you are expected to perform them. I'm not saying turn down trade related courses (like Coyote driver, etc), but if you don't like talking to people that are depressed, don't take Suicide Intervention, as an example. Remember that the military qualifies you for things because there is a need for people to be qualified; they don't do it just because people want to pad their resume.
Having said all that, you should look forward to any training opportunity you can get, as the better educated you are, the more employable you are, within the military, and on the outside once you are done.
A last point: sometimes when you do a course, you won't get a "certificate", even if it is a civilian qualification, because the CF won't pay for it (an example of this is First Aid). Pay the few bucks and stay current, as it will save you some major coin down the road. Another example is Air Brake. After you do the training, go down to the Motor Vehicle department, and write the civilian exam. It'll cost you, but at least you will have the civilian qualification without having to pay for the training (I never did this, and sometimes wish I had).
Hope this helped,
Al