I use a small number of very elite troops to attack plus throw away cannon fodder to soften the target city. I therefore settle my great generals in one city, go Theocracy when army building and I look after, promote and upgrade all early elite axe / mace / etc, but within this elite attack force are defenders with hill promotions. I don't use them to attack or defend cities, and I just use them to keep my attacking stack alive when travelling in enemy territory. My attack stack always travel by hills and by the time the world has railways, my hill defenders have grown in number, and are all highly promoted.
The trick with attacking an overseas civ or any civ for that matter is to understand that they are going to counter attack with a huge stack. Once you have dealt with that stack, then all the the AI can do is build, whip, chop or draft replacements, so if you can absorb the damage of their counter attack, and still keep your elite attacking units in one piece, then you have them over a barrel.
You therefore need to plan the attack so that you are conducting it with both attacking and defending units, and that you are capable or continually reinforcing your troops to replace losses and to secure gains. Allies are very useful, and the geography, (hills, forests, rivers, etc), makes a huge difference.
I usually have two separate attack forces when conducting any attack. The first stack into enemy territory is designed to soak up the counter attack so it contains lots of defender type units, and the second stack is my real city attack force, which I keep well back until it is safe to use them.
One of the largest problems with invasions in the early rail period is enemy arty, as the AI can throw insane amounts of arty at you if they have it. Arty vs your rifle stacks will just cripple you, and it's almost just as nasty against infantry stacks. So, if you are going to invade in the early rail period, then you have to factor in the power of arty. Does the AI have it? Can you attack them before they get it? Do you have it? Do you need it? Etc.
Overseas invasions in the modern era just need a bit more planning, (with or without railways), and the earlier you can do them, the better.
Last but not least, if you are completely stuck by overseas invasions, then plan on gaining an early foothold on the target continent via settling a city there. It will probably be an ice / tundra city, as the AI will have settled all the good land by the time you land, but at least you then have a safe beachhead for your later invasion. This will require you to beeline straight to optics, and you will need to give it a huge culture boost to prevent it from flipping, (settle a Great Artist in it). Needless to say, if you do found a city on an enemy continent, then pay special attention to your diplomatic relations, as it will be weak as a kitten, and almost impossible to reinforce when relying upon early naval transport units.
Regards - Mr P
). Now you have the bulk of his attacking army ( not much of defensive promos ) in a city with no cultural defenses 
... Destroy and move on ( after rushing a airport in captured city if you can : sea reinforcement is so slow in those days ): AI will take some time to recover from that carnage and it may be enough to win the war
) which principles are still appliable... basically:
