Many times I'll use the "pillaging explorer" feint once navigation is discovered. It works especially well if you can land a couple of galleons or transports with equal parts riflemen/infantry and explorers in their backfield. Then march inland, using the rifles/inf to raze tiles they're on and the explorers to branch out, raze tiles, scare workers into the cities, and then duck back behind the guards. If you have cavalry, you can mix a couple of those in for token offense/worker kidnappers. Try and nail their resource tiles too.
The AI will generally freak out and use its attackers against the rifles/inf. and leave your main invasion force largely unmolested. They will also be less prone to try and reinforce cities you can't get the main force to in the first few moves of the war. Even better, you can save your arty/bombers for taking out the city defenders, and there is no "mission failed" when you raze with units vs. bomb with arty/air. Try and keep your defenders on mountains or hills for the best results. Even if the AI is strong enough to eliminate the invading force, big deal. Just a dozen or so units, and your main objective should be complete anyways.
The best part is, if you do enough damage to their core with the pillagers, after you have taken a few cities, you can negotiate peace and take the AI for an arm and a leg. Wait the requisit # of turns for peace to expire, and since you have used the time to build oodles of units and the AI has simply been trying to reconstruct their infrastructure, you now have a weaker opponent than before. I've even done this trick using mech inf and explorers, which IMO is the very best combo.
<---- and I just noticed, I hit the century mark sometime recently! Yay, I'm officially a troll!