Council member and Westmere garage owner Ray Stevens said it wasn't the first time birds had been poisoned at the lake. A source at the Bird Rescue aviary told him birds had been poisoned twice in the past month.
Two were poisoned the first time and four the second time, though the aviary employee was able to nurse the group of four birds back to health at his home.
Mr Stevens was offering a $200 reward for information leading to the offenders.
"What do people get, getting their rocks off doing that to birds?" he asked.
"They don't do any harm, it just gives people pleasure seeing them.
"It's really disappointing - what's a poor swan done?"
He said the latest aviary poisoning was two and a half weeks ago. "If they want something big to pick on, come and visit me," he said.
"I would love to see these guys nailed."