Can you furnish the dimensions of that space and where that window roof faces. I'm assuming west. The space may have to be enclosed otherwise the cold air will leak downstairs. The easiest way would be to use heavy curtains to cover the stair banister and stair case but it can be unsafe. A friend covers that space instead with a sliding door over but usefully practical as it is to keep the cold air in, I don't like it as it blocks the air flow by half when opened. But that's just me.

When AC not in use, if that louvre windows are opened, it should be less hot and  that warm air trapped near the ceiling should flow out inducing cross flow and stack effect (bottom to top) ventilation. Only problem is that its quite problematic to close before if rains. Plus the fact that its a high ceiling.

Update: this suits your space more.

The bricks and roof are soaking up heat from the sun and they will reradiate inwards and downwards like an oven.

If the window is not meant to be open, perhaps replace it with a fixed pane and install 12" wall or the neater option a ceiling mounted extractor fan (may need to ensure the air can flow out of the roof space and not stagnate in there) to help with the heat and see if it helps without AC. The current glass pane design is quite redundant as only hot air comes in but can't flow out.

That way you can apply a tint either laminate or liquid gel like Kristalbond on the glass before installing it. They have VLT 70 clear or 60 blue tint which is quite ok.

For AC, multiply the area in sqft with heat load factor of 70-75 to derive the BTU/hr. From there, infer HP required. You might want to try Sonneaire as sun and heat is abundant.

Applying tint would necessitate removing the glass I'm afraid due to the unusual configuration. Otherwise only nearly all of it is tinted. That's why I suggested better to redo in this circumstance. Plan ahead and see what options you can come up with and go with the one you're comfortable with. Good luck!