In Chrome, I've used the 'Create Application Shortcuts' option to add links to apps on my desktop. The appear with their favicon, but when I move them to cairo-dock, the favicon is not recognized, and I'm not sure where to find it.
I had a slightly different problem but with a similar solution I feel. When I created a prism shortcut which I believe is probably treated in the same or similar way.
Once you have it there is a guide here on a couple of different ways to change the Icon on your dock How To – Configuring Cairo-Dock