"There have been a couple of hold-ups. We have had issues with staff. But we have just subcontracted out to a headstone company to do them for us so it's well under way," he said.
Ms Cornthwaite is upset about the delay.
"We are one of the original farming families that lived in Ihumatao Rd. Our families gave permission for ancestors to be exhumed from their resting place.
"To date there are only 19 headstones out of a total 46. That means 27 are unmarked graves after more than five years. This is disgusting.
Ms Cornthwaite said her grandparents, Andrew and Agnes Rennie, had been buried at the original church site.
Their remains were moved, but it was years before their headstone followed them to the new gravesite.
"It took a long time and a lot of visits by me. Their original headstone was finally placed [in] March 2010. The headstone was not changed; it just had to be reassembled, which may have been difficult due to its size. But we had other family members who were moved and there are still two headstones to be done for them. I told Mr Cummins that I would not be pleased until every headstone was up."
An airport spokesman said the matter was nothing to do with his company.
"It has all been handled by the Methodist Church with the knowledge of Historic Places Trust."
Slow going
Westney Methodist Church:
* Built in 1856.
* Moved in 2007.
* Graves exhumed.
* Remains shifted to Mangere.
* Many headstones not in place.