If you could find or make a mini black hole - and drop it into the Moon, you could make the Moon into a black hole and it would be orbiting the Earth.
I don't recommend this - I'd be one of those arguing that we keep the Moon :).
Coincidentally the Moon is just big enough so that it would absorb enough matter just from the three degree background radiation to counteract energy loss through Hawking radiation. So you wouldn't be in danger from explosive burst of Hawking Radiation.
In the vicinity of Earth it would easily swallow enough matter as it also has the energy from the sun and solar wind, so it should slowly grow. But does not endanger the Earth.
Naturally occurring mini black holes must be very rare as stars don't keep going out.
And they must also be hard to make by colliding particles - as we get hit all the time by high velocity cosmic radiation, far higher energy than any particles we can make ourselves in accelerators, or again neutron stars and the like would be suddenly vanishing as a result of the black holes created by collisions of particles into them.
A tiny black hole could be put in e.g. geostationary orbit. Depends how small it is. But a million metric ton black hole would last a couple of thousand years. It would however be very very hot and so imagine it would be a radiation hazard.
A lunar mass black hole however would be cold. It's 0.0123 Earth masses, so putting that in this calculator:
It would be only 0.1 mm in diameter. So you could easily lose track of it. Also, don't know for sure but I'd guess a black hole so tiny wouldn't have much of an accretion disk either. While being too small to emit much Hawking radiation.
It could be quite tricky to deal with. Maybe satellites orbiting it at a distance to warn space travellers of its presence.
Anyway this is purely theoretical - and I think if you do want a black hole anywhere, maybe asteroid belt is a better place than Earth orbit :). And I think we should keep our Moon as is rather than turn it into a black hole, if it were ever possible :).
And don't need to worry about our space being filled with such black holes - they are obviously so rare that they never come anywhere near stars, at least nobody yet has seen a star vanish as would happen if Moon sized black holes were commonplace.
All this assumes black holes exist, at all, not really proven yet. And if they emit Hawking radiation. And if those figures are correct.
Alternatives to black holes, other things that could form in cases of extreme gravity, include Planck Stars, "Grey holes" and Gravitars. Could Black Holes Give Birth to 'Planck Stars'? : DNews The Gravastar: An Alternative to Black Holes?
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