  A family of diffeomorphism-invariant Seiberg--Witten deformations of gravity
is constructed. In a first step Seiberg--Witten maps for an SO(1,3) gauge
symmetry are obtained for constant deformation parameters. This includes maps
for the vierbein, the spin connection and the Einstein--Hilbert Lagrangian. In
a second step the vierbein postulate is imposed in normal coordinates and the
deformation parameters are identified with the components $\theta^{\mu\nu}(x)$
of a covariantly constant bivector. This procedure gives for the classical
action a power series in the bivector components which by construction is
diffeomorphism-invariant. Explicit contributions up to second order are
obtained. For completeness a cosmological constant term is included in the
analysis. Covariant constancy of $ \theta^{\mu\nu}(x) $, together with the
field equations, imply that, up to second order, only four-dimensional metrics
which are direct sums of two two-dimensional metrics are admissible, the
two-dimensional curvatures being expressed in terms of $\theta^{\mu\nu}$. These
four-dimensional metrics can be viewed as a family of deformed emergent
gravities.
