Mr Pinheiro and Mrs Gordon found a former GP to administer the intravenous vitamin C to Tiago twice a week.
They also have Tiago involved in a free trial of salvestrols, plant-derived compounds which are said to trigger a process in the body allowing it to kill diseased cells.
Their diet is as pesticide-free as possible, and cuts out as much sugar and carbohydrates as Tiago's growing body will allow.
Mrs Gordon said when Tiago was first diagnosed it was not an option to try alternative therapies.
"It has been kind of hinted at that we would end up in court and we would have lost custody of our child."
Mrs Gordon said they would have liked to put Tiago on alternative therapies while he was undergoing regular treatment.
"We would have used them alongside but it is very actively discouraged. Because the treatment wasn't successful it means we are now free to choose the treatments that we want."
She said they chose vitamin C over invasive chemotherapy because it offered hope and quality of life.
Dr Steve Joe, who administers the vitamin C, said studies out of the United States showed high-dose vitamin C was beneficial to cancer patients.
"It hasn't been shown to cure cancer but certainly it makes people feel much better, and gives them a much better quality of life and generally makes their life longer."
Dr Joe, a former GP for 30 years, said the fact it was controversial and not accepted by conventional doctors was unfortunate.
"I think they're very slow to change their ideas. There's a lot of misinformation about vitamin C."
The Cancer Society chief executive Claire Austin said cancer sufferers and their families faced a "horrible dilemma" over treatment options.
"What we would say is that people should always discuss it with their doctor before starting anything that's an alternative because it's very important to make sure there is evidence around those things, and not to give up proven treatments."
To help with Tiago's treatments, go here