Shading a planet



The most effective, long-term method of shading a planet is with moons.

Solar shades
Solar shades have a low mass, high surface-area-to-mass ratio and unstable orbits. Their high surface-area-to-mass ratio allows sunlight to easily push them into a higher eccentric orbit. In a short time they're flung out of orbit or crash into the planet. Their thin material is shreaded my cosmic rays and micrometeorite impacts. They're expensive to produce, difficult to position and require continual maintenance. They're a short-period option, not consistant with the long-period stages involved with terraforming.

Moons

Moons have a high mass, low surface-area-to-mass ratio and maintain a stable orbit.
They promote techtonic plate activity, tides, and volcanism.
They're also essential for moonlight, which many nocturnal species rely on.

When a moon passes between the planet and a star it creates a shadow on the planet, an eclipse. An eclipse will, for a short time, shade the planet from direct sunlight. In the shadow of an eclipse the local temperature plunges. The amount of sunlight reaching the planet, as a whole, decreases slightly but regularly. By maximising eclipses a significant and permanent decrease in tempeature can be achieved, and maintained with no additional cost.

Eclipses are often overlooked as a method of planetary cooling. Perhaps this is due to our own infrequent and brief eclipse experience with Luna. The orbital inclination of Luna is small, 5°, that's enough to keep its shadow off Earth most of the time. If the orbital inclination of Luna was 0°, there would be longer and regular total eclipses every month.

There are many options to maximise the decrease in temperature caused by an eclipse:
0° orbital inclination is essential! The slightest inclination will significantly reduce eclipse frequency and its shading effect. The orbit of any mass in a system is gravitationally effected by other masses, and will alter over time. Minimise this effect by ensuring all masses in the system, especially gas giants, have a 0° orbital inclination.
Have multiple moons. Extra moons will have different orbits and thus different orbital periods. Careful calculations can maximise the number of moons and ensure multiple eclipses.
Create a high volume, low density moon. The larger and lighter the moon, the closer it can move to the planet, and the greater the shading effect. Also, lighter moons mean more moons can fit in orbit of the planet.
Albedo Both high and low albedo moons create an eclipse when on the star side of the planet, but only high albedo moons create moonlight when on the other side. Moonlight will add an extra small amount of energy to a planet but the ability to watch multiple moons dash across the night sky might be worth it. It's up to you.

When lower temperatures are no longer required, a slight increase to the orbital inclination of each moon will significantly reduce the shading effect, and create a spectacular moon filled sky.