I have no clue if this is still helpful to anyone, but I didn't see it anywhere else on the forum so here's the guide "how to get a parkkarte the easy way" for the blue zones in Zürich.
Go to www.stadt-zuerich.ch/parkkarten
Click on Tagesbewilligungen
Click (scroll down) on Tagesbewilligung online bestellen
From there on you fill in the different fields and click on weiter
You'll have to have a Swiss creditcard for as far as I understand to do this and the license plate at hand of the car that will need to park. You get the parking ticket send to you by e-mail, it's bound to the license plate and a date.
After visiting a closed police station (3 times!) and a very exhausting discussion with a gentleman at the traffic office of Zürich I finally figured out that you can do it this way as well. No need to make yourself understandable in German, yay!
Cheers,
Kerstin