Orbital mechanics is not my field of expertise, but the only orbit that keeps something in one spot in the sky (as viewed from Earth, of course) is a geosynchronous orbit. This is pretty much over the equator.

Now, try to make sure that object (assuming its large enough) is between you (on the Earth) and the sun, on a globe with a tilted axis, and you can start to see the problem. I'm not sure it's even possible.

You could have an intermittent ring of objects strung along one orbit that passed over a spot on the Earth, which would reduce the net sunlight over time. This would only work for a few spots on Earth, and shade a lot of spots that wouldn't want it.

A solar sunshade would be stable, and possible, in the "L-1" Lagrangian Point (if I spelled that right, it will be a miracle.) I think this about a million miles sunward from Earth.

Calculating the required size of a shield at that point, leaving aside problems of moving it when you don't want shade, or keeping solar light pressure from shoving it out of its spot, will be left for those with bigger brains than mine.