It is really easy on islands.
Except that, as a rule-of-thumb, you do not what to have to wait until Astronomy to first start. It depends what islands gives you.
So it's highly recommended I do a water or land map, not my usual small continents plus?
Nothing wrong with small continents plus, especially since that is what you are used to. But maybe hold out for a one where you do roll a neighbor? I would think you would want to practice taking a city early with archers and CBs. That is a generalizable skill. The water separation will make things easier, so that is good for your first time going for domination. Divide and conquer, and the ocean helps with the divide part. Plus the AI is terrible at naval warfare.
As for diplomacy, how do you keep them calm?
Clearing your continent early is part of keeping the AI calm. Dead men tell no tales. You have 2x the space of every else, so you play as you usually do, timing your world wide domination push for the unit of your choice. Maybe frigates?
Your first target should be an AI that everyone else hates. Bribe the target to DOW several civs, then DOW the target. Stay at war until you have their cap, and you are confident they cannot recover, but probably do not kill them off. So now you have 2 of 7 caps.
See if you cannot repeat this trick once more, 3 of 7 caps.
Now things are starting to get tense, but you only need trades with one or two AIs. 4-on-1 is harsh, but you can handle 2-on-1. Once ideologies are up, you know how that will shape future relations. So use that to pick your next two targets. 5 of 7 caps, and it is time to take caps from your former allies. I always let the DOFs expire, just for the RP.
Your last couple of strikes might be more surgical, since you only need to hold the next-to-last cap for a couple turns, and if the last cap flips right back -- you have already won!