In the industrial times, your enemies will definitely have fast attack units. The fastest of them are cavalry, which move three squares on unfriendly territory. Here is a strategy for attacking a powerful neighbor with fast troops:
Declare war, but make sure at the end of that turn, all your attackers are shielded with good defendes (riflemen or better). That way the AI will usually ignore them. This is especially true when you lure them with bait. Their favorite is an unguarded city. You see, the AI cheats: they can see well into your borders and know even about interior cities which are unprotected. With cavalry, they can also reach rather far into your borders to attack. So pick a city very carefully: it must be one square out of range of their cavalry. They will almost always make a mad charge for the empty city, stopping one square short of it. In my last battle on Diety, the Germans stacked 26 cavalry just outside an undefended city. They must have thought it was as good as theirs.
However, I brought in artilliery which was waiting in the wings into the city, and blasted the stack with every last shot I had. That hurt them quite a bit. Then I brought in my own attackers. You see, cavalry are fairly bad defenders, especially in open terrain. When my own cavalry moved against them, I didn't lose a single unit. Then I finished them off with miscelaneous troops brought in from various corners of my empire. In a single turn, I managed to eliminate Germany's entire offensive army. I was then able to walk through their land with very little counterattack.
Another effective bait which has often been discussed are workers. The best way to use them, I find, is two squares inside your territory. If the enemy has fast units, they won't be able to help themselves, and make a mad rush for your worker. But then they end up stuck in your territory where you can bomb them at you leisure and finish them off, almost certain your troops will incur no harm. Then use one of your own fast units to recover the worker, who is still on your territory. He can do some work on the very same round!
These strategies are enough to totally neutralize the AI counterattack, even on Diety.