Jakarta to Yogakarta by train

Hi I'm looking to book train travel between Jakarta and Yogyakarta with my family when we come to Java in the summer. I've seen that there is a train with luxury cabins but these are private, single/individual cabins. We're going to be a family of four, two young kids. I'm assuming there aren't private cabins for a family of four. No issues being with other people but my girls can be loud so we would like to have a bit more of a private space. Is this possible on this train route/ journey? We prefer train journeys so don't want to fly.