Change background colour for PDF when Viewing
So Preview does not have this feature, but more on that in a moment.

f.lux

I would strongly recommend you take a look at f.lux.


  f.lux makes your computer screen look like the room you're in, all the time. When the sun sets, it makes your computer look like your indoor lights. In the morning, it makes things look like sunlight again.


f.lux will adjust (you can modify the strength) the colour of the whole screen to make it easier on your eyes. You can set it to be on all the time, or automatically come on at night time. People love it.

Now, back to your question...

Adobe Reader for Mac does support this. Once you install the 400MB app, you can change the background colour in Preferences (⌘ cmd + ,) > * Accessibility** . Check Replace Document Colours, and set the right colours you want.