Pre-main sequence stars are variable sources. In diskless stars this variability is mainly due to the rotational modulation of dark photospheric spots and active regions, as in main sequence stars even if associated with a stronger magnetic activity. Aims. We aim at analyzing the simultaneous optical and X-ray variability in these stars to unveil how the activity in the photosphere is connected with that in the corona, to identify the dominant surface magnetic activity, and to correlate our results with stellar properties, such as rotation and mass. Methods. We analyzed the simultaneous optical and X-ray variability in stars without inner disks (e.g., class III objects and stars with transition disks) in NGC 2264 from observations obtained with Chandra/ACIS-I and CoRoT as part of the Coordinated Synoptic Investigation of NGC 2264. We searched for those stars whose optical and X-ray variability is correlated, anti-correlated, or not correlated by sampling their optical and X-ray light curves in suitable time intervals and studying the correlation between the flux observed in optical and in X-rays. We then studied how this classification is related with stellar properties. Results. Starting from a sample of 74 class III/transition disk (TD) stars observed with CoRoT and detected with Chandra with more than 60 counts, we selected 16 stars whose optical and X-ray variability is anti-correlated, 11 correlated, and 17 where there is no correlation. The remaining stars did not fall in any of these groups. We interpreted the anti-correlated optical and X-ray variability as typical of spot-dominated sources, due to the rotational modulation of photospheric spots spatially coincident to coronal active regions, and correlated variability typical of faculae-dominated sources, where the brightening due to faculae is dominant over the darkening due to spots. [Conclusions not shown in the pre-print]
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