  We characterise, in the setting of the Kodaira-Spencer deformation theory,
the twistor spaces of (co-)CR quaternionic manifolds. As an application, we
prove that, locally, the leaf space of any nowhere zero quaternionic vector
field on a quaternionic manifold is endowed with a natural co-CR quaternionic
structure. Also, for any positive integers $k$ and $l$, with $kl$ even, we
obtain the geometric objects whose twistorial counterparts are complex
manifolds endowed with a conjugation without fixed points and which preserves
an embedded Riemann sphere whose normal bundle is $l$ times the line bundle of
Chern number $k$. We apply these results to prove the existence of natural
classes of co-CR quaternionic manifolds.
