Put the black surface an inch away from the satellite, supported by standoffs. That'll keep the heat away from the satellite.

Also, the black surface only needs to be on the Earth facing side.

It isn't that simple, is it? Even if you place the black surface on a spacer (adding mass, might I add), the black surface itself is going to radiate heat back onto the satellite via blackbody radiation. This is always going to create a worse thermal situation unless you can somehow radiate away as much heat as you could with reflections. To see what I mean, check out JWST's thermal shield.