【Updated: 】
Islands that appear are randomly chosen from all islands you haven't visited yet and islands that still have souvenirs left. On the List of Islands, islands marked with a ☆ will not appear again after they are completed. If you clear all islands that are currently in progress, as well as islands marked with a ☆ symbol, it will be easier for your desired island to appear.
You can check the List of Islands by following the directions below.
■ How to check the List of Islands
① Tap Refresh Islands from Gulliver's Ship screen.
② Tap Details in the upper right corner of the screen.