"We had it in the corner of the front garden," Mrs Oshana said.
"It was April 28. We got up that morning and it was not there.
"It is scary to think someone has seen it and gone after it - come on to our property and taken it."
She said the theft had clearly been planned, as whoever took it would have passed by their Wentworth St property several times and devised a way to remove it.
The buggy would need to have been towed away rather than started.
"And it was taken on a night which was pretty stormy and loud - so we did not hear anything."
She said the children were upset at losing their buggy chum, especially the older boys, who had enjoyed helping dad work on it.
The family moved to New Zealand having decided it was the best place to bring up their family, and to home school them, which they were not allowed to do in Germany.
Her husband had recently started his own business and life in the Bay had been good, Mrs Oshana said.
Having their buggy stolen had been unsettling.
Mrs Oshana said they could not afford to get another one and were prepared to offer a $200 reward for anyone who could help reunite them with it.