by Michael Chan.
I've since realized there is the core_course_get_courses_by_field method that was introduced in version 3.2. Here is the syntax to filter by a category value, but you can also filter by id, course id, short name or category:
https://MOODLEURL/webservice/rest/server.php?wstoken=TOKENVALUE&wsfunction=core_course_get_courses_by_field&field=category&value=[###]&moodlewsrestformat=json
Please ensure the new API method is added as a function to the webservice token so you have the proper access.