It would seem your only option would be to either use compact computer speaker(s) or mount your centre channel speakers to the side of your monitor. If you can fit the desktop speakers underneath the monitor, you could either use just one, or use two but side-by-side. Alternately you could use two at the side of the monitor.
Wired in parallel or series (series would probably work best, as they are likely to be low impedance) in mono they might throw a useful centre channel image. Two speakers in mono and connected to your centre channel output *should* have a central image between the two; that is, the sound source would appear to the listener to come from a point in the centre of the two.
Because the centre channel is primarily a dialog channel in the mix, you can get away with lesser fidelity in that position versus the L and R fronts. Not ideal, but then again your options are not ideal right from the start.
If you don't have some suitable speakers to try, you could temporarily remove the side or rear channel speakers (be sure to un-hook the speaker wires at the amp if no speaker is actually connected, or be sure the speaker wires for the ones you are using for this experiment cannot touch each other, such as if you had speaker binding posts wired at the side or rear positions).
Even if using them would block the screen, go ahead and try it anyway, to check if the centre channel image appears to come from the point midway across the monitor (where a "normal" centre channel would be). Try both side-by-side at the centre position, and also try one each at the side of the monitor. Basically you will be listening to a L - C - R 3-channel setup, but that would be good enough to assess whether it would work to your satisfaction to get around your problem. Of course if you have some compact computer monitors around somewhere that would fit there without blocking the screen, you could try those instead of moving your sides or rears temporarily.
If none of those work for you, or you want to experiment with alternate placement, you could try putting the centre above the monitor on the upper mantle.
Although the above are not ideal, they may work for you considering the limitations you are faced with.
6 cm [2.36"] is a very tight height limit; even a few cm more would help enormously. However you could try a DIY centre channel utilizing compact full-range drivers, you may even be able to use a proper M - T - M configuration. There are drivers available that are 2" or slightly less in diameter. Check Parts Express or Maidsound for something that might work for you. The enclosure rigidity would be adequate due to the compact size even if you had to use 6mm [¼"] material, or perhaps you could find even thinner masonite. Considering your problem, maybe the best solution.
