Letters were sent to those who have placed borders and gravel around the graves asking them to contact the council with a view to discussing the position.
But the relatives claim the new rules - which state they can't leave tributes - were made after they had bought them and are refusing to remove them.
Natalie Brown laid her still-born son Curtis to rest in Glebe Cemetery last year and says she is consulting a solicitor about the situation because being able to place toys on his grave means so much to everyone.
She said: "We put up a surround after the council stopped collecting the grass cuttings and we were having to clean up the grave every time.
"In our opinion, these borders and the gravel make the cemetery look much better and it's our way of keeping it tidy. Under no circumstances will anyone be removing mine."
Ann McColm, from Fairhurst Road, who lost her 44-year-old husband last July, was upset at the council's actions. She said the notice about the new rules had gone up on the cemetery gates recently but were not there when she put down the fence and gravel round her husband's headstone seven months ago.
A council spokesman said: "We appreciate this is a very sensitive issue, so the letters sent recently are the initial approach to lair-holders. The letters have not given formal notice to remove any particular items, but ask the lair-holder to contact us to discuss any items which may not comply with rules.
"There are very good reasons for the rules for managing cemeteries. There are many structures on graves that are inappropriate and intrude on neighbouring graves.
"In some cases, they are potentially dangerous. Such structures on graves can cause problems with maintenance of the cemetery ground, could potentially damage machinery and harm staff and visitors. Planting is not allowed because it could lead to instability of the ground, intrusion on other graves and damage to neighbouring headstones.
"Formal notices will follow the informal letter should the lair-holder fail to contact the council or alter or remove non-compliant items as requested, but we hope that the informal discussions will make this unnecessary."