Thai Buddhist calendar and Japanese imperial calendar systems were added in 1.4 and 1.6, respectively. However, there's no public way to identify those non-Gregorian calendars. You need to rely on a Locale with which a Calendar object has been created. There should be a method to get calendar system identification.
Unicode LDML (Locale Data Markup Language) defines identifiers for calendar types. Java SE should use the same identifiers.