How can I conquer or destroy a city on a single tile island in Civilization IV?

It is all written in the title but an image could help.

How can conquer or destroy this city?

You CAN attack out of boats. There are just some problems with this:

• CORRECTED: The defenders get +50% strength for your units making an Amphibious Landing. (similar to attacking across a river, except that defender bonus is only 25%) This can be removed by taking the Amphibious unit upgrade. This upgrade is sadly level 3: Combat I > Combat II > Amphibious.

  Some units start with this upgrade: Berserkers, the Viking special unit, and Marines (including Navy Seals, the American special unit).

• If I recall correctly, you can not use land units to bombard from ships. You can however: use ships that can bombard, or bombard with aircraft. (OR nuclear weapons late in the game, if it comes to that)

• You can try espionage to weaken the defenses first.

• You can always take over the city with culture, although that doesn't look likely in this case.

You can improve your chances with smart unit upgrades and bombarding, but you're ultimately going to have to attack out of your boats, quite possibly with a lot of units.

I do wonder: Why do you NEED to take the city? If that city (and others like it) are all that's left of a Civ, why not accept capitulation?

EDIT: Pics or It Didn't Happen

Please forgive the size of these pictures. I was not sure how to edit them down without making the combat text unreadable.

Test Setup: I used galleys and gave myself no techs to prove it could happen early in the game. Didn't bother to fortify the defender since that's not important to what I'm testing, but the difference certainly makes this look easy!

Here you can see the dreaded +50%. I wanted to compare the odds of taking Amphibious or an upgrade against a unit type, thus here you see Cover. (+25% VS Archery units)

Here you can see a Maceman with Amphibious, and the dreaded +50% is gone. I was concerned that taking Amphibious was not as good as other upgrades, (when I thought the penalty was only -25%) but it is CLEARLY better, if you can get your unit to level 3.

The payoff:

Notes:

• Please forgive the macemen glowing. I gave them experience AND the upgrades by accident with the map editor, but checked the odds with the upgrades differing by just Cover vs Amphibious.
• Test was done in Beyond the Sword, although I REALLY think this works the same in vanilla and Warlords.
• I initially remembered the penalty was only 25%, which has now been corrected!
• Because I was wrong about the penalty for attacking out of ships, I checked attacking across a river. It is 25% as I thought, I've just corrected the wording to match the wording/effect in the game (25% penalty to you vs 25% bonus for defender.)