Aims. To study the X-ray properties of young stellar objects (YSOs), we analyze an exceptionally sensitive Chandra dataset of the Coronet cluster in the CrA star-forming region, achieving a limiting luminosity of L X,min ∼ 5 × 10 26 erg/s for lightly absorbed sources. This dataset represents one of the most sensitive X-ray observations ever obtained of a star-forming region. Methods. The X-ray data are used to investigate the membership status of tentative members of the region, to derive plasma temperatures and X-ray luminosities of the YSOs, and to investigate variability on the timescale of several years. Results. 46 of the 92 X-ray sources in the merged Chandra image can be identified with optical or near/mid-infrared counterparts. X-ray emission is detected from all of the previously known optically visible late-type (spectral types G to M) stellar cluster members, from five of the eight brown dwarf candidates, and from nine embedded objects (protostars) with class 0, class I, or flat-spectrum spectral-energy distributions (SEDs) in the field of view. While the Herbig Ae/Be stars TY CrA and R CrA, a close companion of the B9e star HD 176386, and the FOe star T CrA are detected, no X-ray emission is found from any of the Herbig-Haro (HH) objects or the protostellar cores without infrared source. We find indications for diffuse X-ray emission near R CrA / IRS 7. Conclusions. The observed X-ray properties of the Coronet YSOs are consistent with coronal activity; soft spectral components hinting towards X-ray emission from accretion shocks were not found. The X-ray emission of the AeBe stars TY CrA and HD 176386 probably originates from close late-type companions. The Ae star R CrA shows a peculiar X-ray spectrum and an extremely hot plasma temperature. Finally, we discuss the differences of the X-ray properties of YSOs in different evolutionary stages.