Justice Katz said the key question for the jury to consider was whether Cooper had intended to kill Jermain.
The Crown had said the incident occurred after the toddler suffered a "toileting accident" and Cooper snapped.
Suffering serious head injuries, 2-year-old Jermain was rushed to Starship Hospital but died five days later.
Crown prosecutor Aaron Perkins QC earlier told the jury that when paramedics arrived at the home they found Jermain required immediate surgery.
"He had a severe head injury, emergency surgery was performed at Starship, but there was no hope - the injuries were too severe," Perkins said.
Jermain died on December 18, 2015, when his life support was switched off.
"The damage had been done," Perkins said. "The entire left side of his brain was effectively dead already. A very bleak picture, indeed."
Cooper had been caring for four of her daughter's children at the time of Jermain's death, all of whom were pre-school age.
Jermain was also described as very small for a 2-year-old, with a weight of just 10.3kg and height of 79cm. He also suffered from learning difficulties and struggled to walk unaided.
The Crown said Cooper killed the toddler because he was too hard to toilet train and she was irritable from smoking methamphetamine.
Perkins argued the grandmother was irritable on the day she killed Jermain, due to her coming down from a meth-induced high and was also getting little sleep.
Cooper's nephew told the court he smoked meth with Cooper, and Perkins further argued medical tests showed her grandchildren had been exposed to the drug.
Jermain's mother, Nadia Ngawhau, told the court early in the trial she was "very disappointed, very sad" and "quite upset" that Child Youth and Family (CYF) had removed her children and placed them with Cooper.
However, she said her relationship with her mother was "great", and from what she saw her children loved their nana.
Cooper also initially blamed Jermain's death on her then 4-year-old granddaughter, whom she claimed hit the 2-year-old over the head with a computer tablet, Perkins said.
A stoney-faced Cooper stood in the dock as her fate was decided. She waved to her family as she was led away to the cells.
Cooper will be sentenced on October 12.