McKeever, 63, of Tamneyreagh Park in Eglinton, was found guilty at Belfast Crown Court last week of eight offences spanning a period from August 1981 to December 1988.
He was suspended from the SDLP when the allegations emerged and expelled following his conviction.
After a jury found him guilty, the SDLP booted him out of the party.
Councillor Tierney said: “Following his conviction for child sexual abuse last week it is time for Jim McKeever to do the right thing and resign his seat on Derry City and Strabane District Council.
“He has been convicted of some of the most horrendous crimes imaginable and he is unfit to serve or represent the people of our city.
“It is deeply regrettable that he has not already taken the decision to stand down.
“I speak for everyone in the SDLP when I offer my support and solidarity to the victim who came forward last week and detailed the ordeal she suffered at the hands of McKeever over a number of years.
“It was incredibly brave to share her experience and I hope it will give other victims and survivors of abuse the strength to come forward and seek justice for themselves.
“While I know it can be a very difficult and traumatic experience, particularly for those who suffered abuse as young children, anyone who discloses abuse will be treated with respect and dignity and directed to the proper services to support them.
“There can be no hiding place for abusers within our society.”Tags: