Hey I just got my coop work permit today actually
My application took 62 days (including holidays and weekends). You find the processing times under "work permit extension new employer", it states 57 days right now.
I strongly suggest that you apply in the next 10 days or so (it's very easy) in case you have an issue, just so you have enough time to reapply if you need to (you probably won't). I applied in November and only got it now
Just so you know, there's no fee if you already have your study permit. I suggest you check the McGill University website, they have a page that explains how to answer properly to the questionnaire on CIC in order to apply for a coop work permit. It worked for me
You will need to get a letter from your university stating that work is a required component of your degree. Talk to the program's people and they will send it to you. You'll also need your passport, a photo like for the study permit, and your current study permit
If you don't have your study permit, then you will apply for the study permit, and on the application form you'll have a box to check to say that you're also applying for the coop work permit. No hassle really, same papers required, you'll just need that letter from the university