I used black out film (what you stick on the window) rather than black out curtains for y daughter.
It worked really well and I left it on for years. Easy to remove when needed.

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Could you hang the black out curtains inside the windows frame? Or if they are already, could you get slightly bigger ones and hang to the wall, and stick down around the edges of the windows?

An awning to the outside?

Maybe use velcro dots along the frame of the window to hold down the curtains.

Put a curtain over the top or flatten a cardboard box and cover the window at night

I have blinds AND block out curtains, works. Could you maybe tack the edges of the curtains to the wall somehow? That works too, as long as it’s not to damaging to the window surrounds

Black paper over your windows. Big sheets stuck together, works a treat!

Providing your curtains are long enough this you can do
extend rod or pole beyond window size it is true
then rehang stops light peeping in at the sides you will see
you have covered window beyond and will now be light free!

Behind you can also use blackout binds (the roller sort) and / or e.g. wooden slat blinds. Sounds like your curtains are not wide enough though – extend the curtain rail a good foot more each side.

The best thing is aluminun foil on the windows or stick the curtains to the wall at the sides where the sun is peeking through.

I peg my curtains together, you can also use a double curtain rod so that you have 2 layers of curtains.

I used to have blinds in and curtains over the top. That always seemed to do the trick.