  For a closed cocompact subgroup $\Gamma$ of a locally compact group $G$,
given a compact abelian subgroup $K$ of $G$ and a homomorphism $\rho:\hat{K}\to
G$ satisfying certain conditions, Landstad and Raeburn constructed equivariant
noncommutative deformations $C^*(\hat{G}/\Gamma, \rho)$ of the homogeneous
space $G/\Gamma$, generalizing Rieffel's construction of quantum Heisenberg
manifolds. We show that when $G$ is a Lie group and $G/\Gamma$ is connected,
given any norm on the Lie algebra of $G$, the seminorm on $C^*(\hat{G}/\Gamma,
\rho)$ induced by the derivation map of the canonical $G$-action defines a
compact quantum metric. Furthermore, it is shown that this compact quantum
metric space depends on $\rho$ continuously, with respect to quantum
Gromov-Hausdorff distances.
