It would have to be a very strange setup.
Having a center channel is most critical when you have seating that's off to the side of the screen rather than dead center. If you're lined up with the screen, the front right and front left speakers should to a good job of simulating sound coming from the screen itself if you have them set up well.
If you are sitting straight on with the screen, I would recommend working on placement of your existing front speakers first (if they're not optimal).
If you are not satisfied with that, or have seating to the side which really makes a center channel necessary, then I would recommend ditching the z-560s and starting over. The z-680s are essentially what you're looking for (or the z-5500s).
If you're going to be making the switch of systems though, I would recommend trying to make a bigger step up in quality. Going from an entry level 4.1 setup to an entry level 5.1 setup isn't going to make a big difference unless the center channel track being centered at the screen is really bugging you.
The z-560s don't have a good plug setup to map onto a 5.1 analog output of a soundcard. You could hook up a single speaker to a small integrated amp or something and have an independently powered and volume controlled speakers as the center. It would probably mess up your bass management though, so it's probably not worth the effort.