The phrase 'cope by' is correct and usable in written English.
It is used to indicate how someone is managing a difficult situation or their emotions. For example, "She is trying to cope by taking some time for herself."
Or maybe you cope by justifying your mistake.
Will we be able to cope by 2050?
But most cope by bending to peer pressure.
You don't cope by fear, and you don't cope by thinking where will all this end up.
Small companies cope by simply dismissing sick workers; rich ones cap their health benefits.
Many adult survivors continue to cope by blocking feelings and trying to forget about the past.
Some are informal, others cope by finding a bit of humour".
They are trying to cope by finding homes for the kittens that are born, she said.
Don't try and cope by staying in, drinking more and exercising less.
India's leaders try to cope by criminalizing neglect of one's parents.
I learned to cope by always trying to talk to or greet someone when it occurred.
