The [Hinode][1] satellite has an active x-ray telescope that is routinely used to image the sun.  And the [NuSTAR][2] extreme x-ray telescope can also be used for sun imaging (although its main job is looking for black holes) 

There are also Extreme Ultraviolet telescopes (at 171Å that is less than an octave away from the conventional lower end of X-rays at 100Å) SDO. Stereo (Ahead) and SOHO all have EUV telescopes. The Atmospheric Imaging Assembly on the [SDO][3] satellite has sensors for wavelengths as short as 94Å, conventionally classed as X-rays

https://www.nasa.gov/jpl/nustar/searing-sun-seen-in-x-rays


  [1]: https://en.wikipedia.org/wiki/Hinode_(satellite)
  [2]: https://en.wikipedia.org/wiki/NuSTAR
  [3]: https://en.wikipedia.org/wiki/Solar_Dynamics_Observatory