Shirl and Jerry Rowley's twin sons Matthew and James died prematurely at 24 weeks' gestation nearly 16 years ago.
Mrs Rowley explained the memorial wall would be for babies lost for whatever cause.
"It's a pain that never, never goes away, but it does lessen," she said.
Mrs Rowley spoke of her discovery of the Baby Memorial Garden at Anderson's Bay Cemetery in Dunedin, and the pride she and her husband have in seeing their sons' names there.
A similar memorial in Wanaka would be valued.
Matthew and James "were people and still very, very much part of our family", she said.
Mrs Rowley suggested a stone wall could be designed in a half-circle or heart shape to give a feeling of being embraced.
She knew of quarry owners, artists and stone workers who would be prepared to help.
"It does not have to be a huge wall; just something secure, snug. It doesn't have to take up a lot of area," she said.
Cr Lex Perkins acknowledged the grief of parents when their children died, saying his son had died at sea and his family had nowhere to visit and remember him.
Other parents had lost children in the mountains. Could there be room for others to be memorialised, he asked.
Mrs Rowley said she had not considered that but would not say no to any bereaved parent.
Mayor Clive Geddes acknowledged Cr Perkins' suggestion should also be addressed, perhaps separately from the idea of a baby memorial wall.
The council would consider Mrs Rowley's proposal next week and get back to her soon with its decision, he said.
Mr Geddes said Mrs Rowley's suggestion was "very special", and said she would be involved in any future project.
"I can sense around the table there's a great deal of sympathy," Mr Geddes said.
