"A majority of council tenants surveyed last year were in favour of having a pet because of an animal's ability to help with feelings of isolation or loneliness," he said.
"A pet can also assist with social interaction between tenants in our housing complexes and may help residents to remain physically active.
"If residents would like to have a pet during the trial period, they'll need to sign a pet care agreement accepting responsibility for their animal's care and wellbeing, along with any damage the pet may cause to their unit."
Johnston said the agreement would also provide vet details and a contact person who could look after the pet if necessary.
At the end of the trial, tenants who participated would be allowed to keep their pets.
The trial will help the council identify any issues with pets at a relatively smaller scale before a final decision is made on pet suitability at other council-owned housing complexes.
The trial will also help the council understand how best to avoid the possibility of separating a pet from its owner if that person becomes a council tenant.
The council's long-standing policy of not allowing pets in pensioner housing caused a stir in 2019 when some residents were asked to rehome their pet birds or face a 90-day eviction notice.
The threat of eviction was withdrawn and tenants with existing pets have been allowed to keep them while a review was conducted.
The policy and bylaw committee also approved other changes to the pensioner housing policy.
The policy was renamed the "Older Persons' Council Housing Policy" and a process to allow the council's property team to make minor updates to the housing guidelines was approved.