How to fix blank icons for Download and Documents stacks in the Dock

I'm getting blank icons for stacks (e.g. Downloads) and grids (e.g. Documents) in the Dock. Nothing seems to fix it. Have tried relaunching the Finder and even a full reboot, but nothing helps. Any ideas?

There's a question about exactly the same problem from a while back but that's no help as the OP said that upgrading to Mountain Lion fixed his problem.

I'm running Mavericks (10.9.2). Problem started recently, but I can't tie it definitely to the 10.9.2 update.

UPDATE: tried restarting the Dock and that got back 2 or 3 icons, nothing more.

Here's an example of the problem:

Try removing PDFs from the stack's contents. _Source

If that doesn't work, try backing up and removing ~/Library/Preferences/com.apple.dock.plist and relaunching the Dock (killall -HUP Dock).