The judge sentenced Cooper to life imprisonment with a minimum term of 14 years and six months.
Cooper will be 80 when she can be released.
Jermain, lovingly known as Tiger, died after he likely had a "toileting accident" and Cooper snapped, throwing him down the hallway, the court heard.
He suffered serious head injuries and was rushed to Starship Hospital but died five days later on December 18, 2015, when his life support was switched off.
Experts agreed Cooper must have thrown the toddler with "extreme force", Justice Katz said.
Jermain was a small 2-year-old, weighing just 10.3kg and 79cm tall.
He had learning difficulties and struggled to walk unaided.
Crown prosecutor Aaron Perkins QC told the jury paramedics 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," he said.
"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.
Cooper told police that she had phoned for an ambulance immediately after discovering Jermain's injuries, but telephone records show otherwise.
She also blamed Jermain's death on her then 4-year-old granddaughter, whom she claimed hit Jermain over the head with a computer tablet.
The legal guardian for Jermain's sister told the court today that the young girl has undergone counselling as a result of her brother's death.
The "beatings and blatant lies" have scarred a small, innocent child, the court heard.
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, on the day she killed Jermain, was coming down from a meth-induced high.
Cooper's nephew told the jury he smoked meth with Cooper, and the court further heard that medical tests showed her grandchildren had been exposed to the drug.
Jermain's mother, Nadia Ngawhau, told the court at trial that she was "very disappointed, very sad" and "quite upset" that Child Youth and Family (CYF), now known as the Ministry for Vulnerable Children - Oranga Tamariki, had taken her children.
Cooper's lawyer Paul Dacre QC said today that CYF must have decided that Cooper was an adequate caregiver for the children.
Ngawhau also told the jury her relationship with her mother was "great" and her children loved their nana.
However, Dacre added there was increasing pressure from caring for the children and an increasing lack of ability to cope with that pressure.
Justice Katz said Cooper was a "harsh disciplinarian" who smacked the children with her hand and at times a belt.
Child care workers also noticed bruising on the children, and a pathologist noticed bruising on Jermain's body.
"This was a catastrophic event, a grandmother was responsible for the death of her grandchild," Dacre said.
He said Jermain's death was an absolute tragedy and his client "takes the legal and moral responsibility" for her grandson's death.
