  We use the embedding of Einstein gravity with cosmological constant into
conformal gravity as a basis for using the twistor action for conformal gravity
to obtain MHV scattering amplitudes not just for conformal gravity, but also
for Einstein gravity on backgrounds with non-zero cosmological constant. The
new formulae for the gravitational MHV amplitude with cosmological constant
arise by summing Feynman diagrams using the matrix-tree theorem. We show that
this formula is well-defined (i.e., is independent of certain gauge choices)
and that it non-trivially reproduces Hodges' formula for the MHV amplitude in
the flat-space limit. We give a preliminary discussion of a MHV formalism for
more general amplitudes obtained from the conformal gravity twistor action in
an axial gauge. We also see that the embedding of Einstein data into the
conformal gravity action can be performed off-shell in twistor space to give a
proposal for an Einstein twistor action that automatically gives the same MHV
amplitude. These ideas extend naturally to N=4 supersymmetry.
