Nobody seems to use the marines, yet they are the most interesting units you can use for an island assault in modern times.
Here's the trick: have transports loaded with modern armors, marines and mech inf (or infantry). Get a battleship to escort the pack (though, if you are not at war yet, it's not that important), and bring a carrier with bombers.
The typical layout would be 3 transports with modern armor, and one with marines + mech inf, depending on the enemy current defensive force (bring more marines if he's got infantry or better to defend). Bring more modern armors too, if the continent is big, bring more mech inf if you plan on keeping the cities ...etc
turn 1 : declare war, bombard the target coastal city to soften defense.
Launch the marines against the city, (hopefully capture it). Bring all the transports in, and unload all the MA. Now, you can activate all the MA on the same turn

Raze all the immediately surrounding cities to prevent culture flip.
turn 2 : go for the kill ...
Of course, chosing the best coastal city to capture is mandatory, you will try to aim for a small one, possibly surrounded by hills or mountains to prevent fast counter attack. And, if possible, you should try to attack two or more spots at the same time to prevent massive counter offense.
As for the early eras, well, just a bunch of troops in galleons... Not much else you can do really.
I am a big fan of beach assault, since I am usually alone early on my continent
loki