What color shade sail is cooler underneath?
My first reaction on this quest was to ask myself is, am I cooler or hotter in a black T-shirt vs. a White T-shirt…
A black T-shirt is obviously hotter. Then some thinking began. If you wear a dark-colored shirt, you get hotter because the color absorbs more UV rays.

So.., white reflects heat, black absorbs it. Darker coloured fabrics are better at blocking UV rays than lighter ones. So a dark blue, green, or black would be better than yellow or white.

Since the canopy isn’t in direct contact with your body the black fabric will block/absorb more of the sun’s UV-radiation than a lighter colour. A shade sail fabric is thin enough that it is going to allow some amount of radiation to pass. So the more important question is which colour is better at blocking this radiation. The black fabric is certainly going to be hotter to the touch, but since you are at least a meter under the sail it does not reflect the heat on your body.

Black shade sail blocking more UV radiation

What about reflection of the radiation?
Darker colours generally block more light creating more shade and a darker environment under the sail. A darker environment will reflect less radiation than a lighter one.
If you are in the shade but close to a reflective surface, such as a swimming pool, shiny white wall or white outdoor table, you may still be exposed to UV rays that bounce off these surfaces. Anything that causes a glare in the Sun (e.g. snow, water, white surfaces) has the potential to increase your UV exposure by reflecting and scattering radiation from any direction – including beneath the shade sail.
So to bring all this together, the best shade sail will have a dark coloured tightly woven fabric.