How can I keep my rats quiet during the night?

Sorry to break it to you, but rats are generally nocturnal (yes, I know you know that). There is really little you can do about it as it is a part of their nature.

You are wanting them to be something other than what is in their nature. I suggest you take them back to the pet shop or find them a new owner.

Well as I see it you can either use a glue trap. But thats messy.
Tie down their hands and feet. But they may chew their way out.
Give them to someone else who may like rats.
Buy a snake.
Or you can purchase a sound machine and get use to hearing a sound slightly louder than the rats but can still let you sleep. Maybe even the sound of a fan blowing.

Back to the pet shop or ear plugs. Rats are nocturnal.

Then get used to it.

Rats are nocturnal.

Do you have a wheel in their cage? If so, you can make it a bit quieter by attaching it to the top of the cage with tie-downs

Leave a cat with them all day so they get no rest.

Earplugs and/or a white noise machine comes to mind.

BTW this is a pretty cute question.

Cheese?

Did you research the animals you took in before getting them?

Give them to someone who doesn’t mind the noise. And go for a gerbil next time, they’re primarily diurnal. (But do your damn research on them too.)

If you can’t give them up, invest in a white noise machine, a fan, ear plugs or suck it up. You will adjust if you just stick it out.

You can only adapt to the noise.

Can’t you put a light in their cage at night so that they will think it’s daylight? In the morning turn out the light and cover the cage so that they will think its nighttime.

I once saw a “Far Side” cartoon with a very haggard looking parakeet who’s owner was getting ready to put a sheet over the cage that had pictures of mean looking cats on it… ;)

sedate them.