He was ordained as a priest in New Zealand in 1979 and left the church in 1997.
Cunneen appeared via video link on Thursday with two of his alleged victims present in court.
Prosecutor Ben Rutzou opposed bail saying there was a risk Cunneen could interfere with witnesses.
"There are no bail conditions the court could impose that would address these concerns," Rutzou said.
Payton told the court Cunneen hadn't had contact with the victims since the late 1980s so wouldn't be seeing them.
He also noted Cunneen had been granted bail in New Zealand after he was arrested and before he was extradited.
The magistrate granted Cunneen bail on a surety of $30,000 cash and a mortgage-free property worth $600,000.
He had to hand in his New Zealand passport and must report to Blacktown Police Station twice a week.
Two of his alleged victims told NZ Newswire outside court they were "very disappointed" he received bail.
"It's taken nearly 30 years to get us here today," one said.
"We thank the royal commission ... we are relieved Cunneen is back on Australian soil."
Cunneen is due to reappear in court in early February.
- NZN