Happened to my initial runaway Alex when I was Rome, start of Industrialization (teching the same), he had at least 10 CS allies by my last count, and AI being AI, gets a near perfect coup each time I successfully coup or buy my way into a CS (even with +104 influence he can coup no problem without death lol). I made a mistake of DoWing him forgetting that my other cities has his CS ally around my border. Suffice to say, I wasted a lot of time fending off CS instead of actually warring Alex.
Since you are on the defensive and not knowing when Alex attacks, your option really is to start pumping units to go on offensive. I suppose as GK you're going for a domination victory anyway.
Best way is to go on offensive, and right before you are about to DoW him, either try to coup the CS or buy yourself into it. Attacking them is just going to negative diplomatic effect and I'd assume since they are under Alex's protection, he'll DoW you regardless.
Out-teching him, and getting advanced units is really the way to go. Else, you would have to suss out a different victory path.