History of Siquijor
WorldCat is a global catalog of materials, containing tens of millions of books, records, and photos. Not all are available publicly, but for the ones that are, the site provides direct links to the relevant databases as well as the closest library that has them. Of these four resources, it's the best place to start.
JSTOR focuses more on research papers than historical documents (although those are often available too). You'll have to create an account to view most items, but it's free and gives you full access to 100 articles a month. If you're affiliated with a college or university, you'll have wider access to JSTOR's archives (community colleges' access unfortunately tends to be less reliable).
HathiTrust is an online archive containing millions of digitized documents. Unlike WorldCat, most things you find there are available publicly and in their full form.
The Library of Congress is the national library of the United States. Of course, its archives focus mostly on American records, but many pertain to the Philippines as well thanks to its American colonial past. That's especially important given how many Filipino documents were destroyed by the Japanese during World War II. Most records found here are digitized and publicly available in their entirety.
Most of my research has been through digitized archives, allowing me to access literature and records from throughout the past 300 years. I began with Google Books. I didn't ever expect to find documents as specific as censuses or war reports there, yet I was able to find all that and more. Tens of millions of written records await with this easily accessible, yet admittedly somewhat finicky resource. It's important to note that not every record is available in its entirety due to copyright. For some, only snippets are available, while others are wholly unavailable. In these cases, the resources below may have the full content of the work in question.
I also relied on the books of the late historian Caridad Aldecoa-Rodriguez, whose comprehensive work on the history of Negros Oriental includes a great deal of information on Siquijor. A much younger me purchased those books years ago at Silliman University's bookstore on a whim. They're likely still available either there or elsewhere in Dumaguete.
From there, I widened the scope of my research. I came to rely on four websites: