A sub-Moon-mass singularity of 1e22 kg provides an acceleration of 9.8 m/s^2 at a radius of 261 km, while having a Schwarzchild radius of 1.5e-5 m.
The combined system of that singularity plus a hard spherical shell at radius 261 km (anchored by some sci-fi means that does not contribute significant mass) has a density of 134 g/mL, 6 times as dense as pure osmium, but being mostly empty space inside. And having a surface area of 856000 km^2, 0.6% the land area of Earth. Such a body could retain an atmosphere and sustain ecological cycles.
