JSTOR - Contains the following journals that would relate to the Crusades and the Latin Kingdoms: American Historical Review, English Historical Review, Past and Present and Speculum. In addition to these journals, there are a number of e-books that would be useful.
REMEMBER: JSTOR treats annual conference proceedings like books, so don't limit your results to articles only. You may miss out on a good article from a conference proceeding or a collection of essays. Also be aware that JSTOR doesn't always provide complete coverage of a journal.
Historical Abstracts - Will give you all of the titles in JSTOR plus access to some smaller, more specialized journals. Just remember to restrict your results to academic articles only. Historical Abstracts provides magazine and non-peer reviewed articles too.
Wiley Online Library - Wiley provide access to these two important journals:
Medieval History Journal - This journal tends to focus on non-European medieval history but it does include articles about the Crusades and the Latin Kingdoms, as well as Islamic kingdoms in that region.
Crusades (A journal that Ashgate publishes this journal for The Society for the Study of the Crusades and the Latin East. Siena does not subscribe to but a listing of issues and their tables of content can be found here: https://www.routledge.com/Crusades/book-series/CRUSADES. Any articles you find can be requested through ILL.
ITER: Gateway to the Middle Ages and Renaissance - This database will provide you with article citations but has no full-text. Any citations that you find you can request through ILL.
Journal of Medieval Military History - (A journal that Boydell and Brewer publish for the Society for Medieval Military History. Siena does not subscribe to it but a listing of issues and their tables of content can be found here: https://boydellandbrewer.com/series/journal-of-medieval-military-history.html. Any article can be requested through ILL.