  Shape and frequency-shift map of direct and indirect images of Keplerian
discs orbiting in Bardeen and Ayon-Beato-Garcia (ABG) black hole and no-horizon
spacetimes are determined. Then profiles of spectral lines generated in the
innermost parts of the Keplerian discs in the Bardeen and ABG spacetimes are
constructed. The frequency-shift maps and profiled spectral lines are compared
to those generated in the field of Schwarzschild black holes and possible
observationally relevant signatures of the regular black hole and no-horizon
spacetimes are discussed. We demonstrate that differences relative to the
Schwarzschild spacetimes are for the no-horizon spacetimes much more profound
in comparison to the regular black hole spacetimes and increase with increasing
charge parameter of the spacetime. The differences are stronger for small and
large inclination angles than for mediate ones. For the no-horizon spacetimes,
the differences enable to distinguish the Bardeen and ABG spacetime, if
inclination angle to the distant observer is known. We also show that
contribution of the so called ghost images to the profiled lines increases with
increasing charge parameter of the spacetimes.
