Mr Betts was off-duty, in a room in the embassy compound's accommodation block.
It was the end of his eight-week deployment and Mr Betts was due to travel home to his wife and parents in Hervey Bay, Queensland, the following day.
He and another contractor Sun McKay had been playing online computer games and drinking.
Just before 2.30am Mr Betts picked up Mr McKay's loaded Glock handgun, held it next to his head and pulled the trigger.
The death initially appeared to be suicide, according to reports through the Department of Foreign Affairs and Trade.
Speaking outside court, Mr Betts' father Colin Betts said the coroner's findings were what he had expected.
"In our hearts we always knew that our son Chris would never have taken his own life deliberately," he said.
"And yes, it appears it's been a tragic accident."