Well, if we want to stick to things with a speed of c, that basically means we're limited to light/radio, gravity (way too weak to be practical), and... some sort of communication based on the strong force? I don't know enough to speak regarding the plausibility of that, but I imagine the fact that gluons can directly interact with other gluons would be a problem.

...barring, of course, some sort of radical new discovery, which I guess was more the point of the question.