The phrase "accustomed way" is correct and usable in written English.
It can be used to describe a method or manner that someone is used to or familiar with.
Example: "She completed the task in her accustomed way, demonstrating her expertise and confidence."
Alternatives: "familiar method" or "usual manner".
It takes a great deal to drive them out of their accustomed way of doing business".
They would lose capital already ventured; they would lose experience already bought; they would suffer the pains incidental to the sudden and enforced abandonment of an accustomed way of life.
That course would have served to determine every question of constitutional law raised by the suit in the Federal court in an orderly way, without trampling upon the state, and without interfering, in the meantime, with the operation of the railway property in the accustomed way.
Until the breakout by the Americans today, it had been possible to believe, if only just, that the Iraqi minister, Muhammad Said al-Sahhaf, might not be whistling Dixie, in his accustomed way, when he predicted that the Americans would be slaughtered in a huge Iraqi counterattack.
The accustomed way of telling stories here had been through the perspective of upper-middle-class intellectuals, civil servants, those with public functions whose job it is to "save the poor from themselves," "enlighten" and "educate" them.
I loved the sound it made, the precise speed to which I had become accustomed, the way it echoed the rhythms of my thoughts.
"One gets accustomed to ways of looking at things, so we turn to these devices when our view of the world has been deadened or crusted over with ennui".
Ms. Figueroa-Levin said she had no problem enunciating Spanish words; her mother is Jewish, but her father is Puerto Rican, so she grew up accustomed to the way the language sounds.
The Japanese, by and large, aren't accustomed to the way of an American reporter; it is unusual for them even to invite friends over for dinner, to say nothing of a gaijin with a tape recorder and a notebook.
Yet changing Instagram's feed will most likely be tricky and may arouse the ire of fans, who are accustomed to the way their photos and messages are ordered.
The system is now so ingrained that it has led to debates over whether it provides an advantage for the best players, who spend more time on show courts and have grown accustomed to the way it works.
