Add a black umbrella to each satellite: when they pass through the critical region where they are visible in the night sky while still being sunlit, pop the brollies up. We will fly them in the shade!
You could paint them black but they’d probably get quite hot.
Won't the shade then reflect the light instead? It's nighttime, so sunlight will be aimed up, from the Earth-based observer's point of view, so the shade will need to be pointed down in order to shade the satellite.