The disc formation mechanism of B[e] supergiants is one of the puzzling phenomena in massive star evolution. Rapid stellar rotation seems to play an important role for the non-spherically symmetric mass-loss leading to a high-density disc- or ring-like structure of neutral material around these massive and luminous objects. The radial density and temperature structure as well as the kinematics within this high-density material are, however, not well studied. Based on the high-resolution optical spectra of a sample of B[e] supergiants in the Magellanic Clouds we especially searched for tracers of the kinematics within their discs. Besides the well-known [O i] lines, we discovered the [Ca ii] λλ7291, 7324 lines which can be used as a complementary set of disc tracers. We find that these lines originate from very high density regions, located closer to the star than the [O i] λ5577 line-forming region. The line profiles of both the [O i] and the [Ca ii] lines indicate that the discs or rings of high-density material are in Keplerian rotation. We estimate plausible ranges of disc inclination angles for the sample of B[e] supergiants and suggest that the star LHA 120-S 22 might have a spiral arm rather than a disc.