A brief history of international Amoy
First let's clear up the various different English versions of Amoy's name.
Traditionally, though Chinese pronunciation varied according to your dialect, everyone wrote things the same way. So, the place we're talking about is 廈門. If you lived there you spoke the local dialect of Hokkien, and pronounced it something like "Amoy". If you're from Beijing you say "Xiamen", today's official name. And if you're Cantonese it sounds like "Ha-moon". Just to add to the fun, in simplified Chinese it is now written 厦门.
I'll use Amoy.
First contacts with the West
Amoy has a long history of international trade. The Japanese and Portuguese were already trading here in the 16th Century, and the 17th century saw the the Dutch join in. 
The amount of trade rose and fell according to Beijng's policies of the time, but by the 19th century the port was well known to international traders.
Amoy becomes a Treaty Port
When Pottinger arrived in Hong Kong in 1842, one of his tasks was to open up more Chinese ports along the east China coast to British trade. 
With this in mind, his expedition headed north from Hong Kong on 21st August, 1842. Their first destination? Amoy.
Initial impressions were not good, with well-constructed defences visible on the smaller islands, the beaches, and the city of Amoy itself. However the British attack met little resistance, and the City was soon in their hands. 
The expedition continued north, notching up several more military victories. These led to the Treaty of Nanking . In the Treaty, China conceded Hong Kong to the British, and also gave the British rights to trade in five ports – the first of the Treaty Ports. Here they are on a map, running along the length of the China coastline:
B. Hong Kong
But where will the foreigners live?
To answer that question, let's take a closer look at Amoy:
The Chinese city (Marker 2) was, and still is on the main island. A short distance away is a smaller island, Kulangsu (Marker 1), now known as Gulangyu (Hokkien / Beijing pronunciation at work again). Kulangsu had first drawn British attention as the site of a large battery of 76 guns, guarding the entrance to Amoy harbour. But "Luckily for the British, the guns on Kulangsu were clumsily mounted and poorly serviced." 
After taking Amoy, Pottinger's expedition headed north but left behind a garrison of 300 troops based on Kulangsu island. That must have been a reassuring sight if you were a foreigner in town. Sure enough, by 1844 Jardine's agent in Amoy, Captain Forbes, had built a house on Kulangsu, and other merchants had followed. When the first British Consul, Captain Henry Gribble, requested that he be allowed to build a house there too, it seemed that Kulangsu was set as the location for foreigners to live.
But the second Consul, Alcock, had different ideas. He wanted to see the Consulate built on the main island, and so have the British flag flying within the old city walls. He got what he wanted, and the new consul's residence was completed in Amoy city in August 1845.
Despite this, and the fact the garrison had moved out in March the same year, Kulangsu remained the preferred location for foreigners to live. "Years later, the point of residence in the city having been gained, the British consulate was moved back among the pleasant breezes and vistas to be enjoyed on the [Kulangsu] island, which formally became an International Settlement in 1903". 
The Japanese take charge
In 1895, nearby Taiwan was ceded to Japan, increasing their influence in the Amoy area. By 1937, Japan and China were at war, and in 1938 the Japanese captured Amoy after an amphibious landing. 
For several years the international settlement on Kulangsu continued relatively untouched... Then: "At 4 A.M. Monday morning, December 8, 1941 armed Japanese Marines crossed the narrow harbor from Amoy and landed in the International Settlement of Kulangsu. With the aid of Consular police and Formosan interpreters began to round up all American and European Nationals. " 
After Japan's defeat in 1945, at least one missionary returned to Kulangsu in 1947, and stayed on "until expelled in October, 1951" . I'm not sure whether there was a serious effort to by businesses to re-establish themselves on Kulangsu. Even if they did, they would have suffered the same fate as the missionary, and have been pushed out sometime around 1949-51.
The title 'Post-war' on the previous paragraph didn't really apply to China, as the end of the fighting between Chinese and Japanese just meant an increase in fighting between communist and nationalist Chinese.
As the nationalists retreated to Taiwan, they left large garrisons near Amoy, on the islands of Kinmen (Marker 3 on the map above) and Matsu. They repulsed the communists' attack in 1949, and to this day the islands remain under Taiwanese control.
During the cold-war, there were regular artillery exchanges between the communists and nationlists. Fortunately, though Kulangsu must have been within range of Kinmen, it doesn't appear to have been a target of the Nationalist guns.
Today the local government recognise the island's value as a tourist draw, and recently announced their desire to get the island listed as a UNESCO World Heritage Site. 
- Trade and society, the Amoy network on the China Coast, 1683-1735
- SIR HENRY POTTINGER AND HONG KONG, 1841-1843
- Sir Henry Pottinger: first governor of Hong Kong By George Pottinger
- The Treaty of Nanking
- Trade and diplomacy on the China coast: the opening of the treaty ports ... By John King Fairbank
- Axis history forum
- Theodore V. Oltman, M.D.--RCA's Last Missionary in Amoy
- Gulangyu to apply for World Heritage Site