I had an eye surgery a while back and needed to black out a room under similar conditions. Though in my case it was the morning sun I was trying to black out.
I have tried 2 methods.
Do you care if its visible from the outside? I used tin foil taped directly on the window. Blacked out completely.
However, people will notice the crazy person with newspaper or tin foil on their windows.
Annoyingly, like Willeke says, the tape does leave behind residue that I had to scrap away with chemicals.
Also, on hotter days there was a fair amount of condensation between the foil and the window. Just a heads up nothing really to worry about there I believe.
I eventually made a shade the size of my whole window out of cardboard. The window was recessed so I would snug it against the top and bottom ledge, in front of the existing ineffective blinds. Blacked out completely.
The nice thing about this is that I could take it down and put it up easily. It left no trace of having been there. And I didnt look like a crazy person; at least from the outside. And it didnt cost me anything since I had cardboard lying around from various amazon packages. Maybe a few dollars in duct tape though.