It follows a Scarborough Council report into cemetery provision in the borough which warned that existing sites could be full within the next four years.
In order to address the problem a derelict football pitch off Larpool Lane in Whitby has been identified.
At a meeting of the council's Lives and Homes Overview and Scrutiny Committee today a number of concerns were raised about the plan.
Whitby Cllr Alf Abbott said the site was used by local people.
He said: "That area now is more important for the recreation of the east side of Whitby than it was 10 years ago."
He said that the residents on the east side of town had a "virtually nil" amount of green space near their homes.
Cllr Abbott added: "The residents on the east side have a right to green space and if that is the only a little bit left then they deserve that."
He said that the council should instead look to use land next to Whitby Golf Club as a new cemetery.
Resident Robert Stevens also told councillors that the golf club land should be considered.
Another resident, Stephen Hinchliffe, said the roads around Larpool Lane were a "traffic trap" where divers were "taking their lives in their hands" trying to get out of junctions.
Whitby councillor, Glenn Goodberry, also pushed for the golf club land to be considered.
He said: "From an access point of view [Larpool] is an absolute nightmare.
"There is a tiny car park where you can get four cars in.
"The Love Lane site, the golf course site as it is called, is served on Love Lane by a bus stop.
"It is served by another bus stop on White Point Bridge and it has two way traffic with much wider roads and far better access."
Cllr Sam Cross said the council should change its mind before it starts consulting with the public.
He said: "The representations that have been put forward by the speakers clearly say to me that what we are proposing is the wrong site and the correct site is the golf club."
A report prepared for the councillors noted that the council's current cemetery sites at Larpool (Whitby) and Woodlands (Scarborough) will reach capacity in the four years time.
The Lawns cemetery in Filey will be full in around eight years time.
Another issue for the authority is that Sport England is likely to oppose the loss of the football pitch in Whitby.
However, council officers believe the objection can be overcome due to new facilities that have been built nearby.
The council's cabinet are due to be asked when it meets next month to send the cemetery proposals out to public consultation.
The overview and scrutiny committee voted today to ask the cabinet to not move forward with the Larpool Lane site and instead look at the land at the golf club.
Earlier this year the golf club site favoured by the committee was included in a joint venture created by the council to provide affordable housing across the borough.
The committee supported in principle two pieces of land next to the existing cemeteries in Scarborough and Filey to be used to provide more burial space.