A kind and learned reader, intent on salvaging grammar from the ambient wreck of culture,  suggests the following:

Ze (Zee), Zem, Zis, Zi, Ze (Zay) –  Ze-Ze, Zem-Zem, Zium, Zibus, Zibus.

The North Country version could be:  Zoo, Zem, Zi, Zay – Zoo-Zoo, Zoo-Zoo, Zow-Zow, Zow-Zow

Permissible dialect spellings: Tse, Tsem &c or Cze, Czem, or for Chinese speakers  Xe, Xem &c.