Councilman Brian Coleman had nominated Michael B. Jordan, who was vice chairman and whose term expired in September 2013, but withdrew Jordan's name at the start of the meeting. That move angered the authority's chairman, Angel Alamo, who stormed out of the council meeting.
Sheila Davis, a clerk with the county Metro Police Department and president of Neighbors of Lanning Square West, was nominated by Councilwoman Dana Burley and had the backing of the mayor but was also not appointed.
The five-member commission is appointed by the City Council and oversees all operations of the independent agency, which is expected to build two parking garages in coming years to accommodate city development projects.
"I am very disgusted and very disappointed. Jordan was one of the best commissioners I have worked with," Alamo said following the meeting. Jordan was not present and Davis declined to comment.
Council President Frank Moran said Davis and Jordan would be considered for positions on other city boards.
"We're going to need people who are passionate and committed and willing to put in the time and sweat equity," Moran said.
Members of the public said the vote showed a clear division between the council and the mayor.
Ali Sloan El, a former councilman, pounded his fist against the podium and yelled at council members for failing to appoint Davis. He said the move amounted to infighting between council members aligned with Moran and the county, and those more closely aligned with the mayor.
"You're out of order when you're out of order with our mayor," Sloan El said. "You're all playing games."
Dorothy Burley, mother of councilwoman Dana Burley and a former city clerk, said she was "bewildered and outraged."
"Don't take people who have worked hard to get you elected and then throw them in the trash," she said. "The mayor and council should be together,"
"We are," Moran said.
"I don't feel that way, Frankie," Burley responded.
Following a meeting of an unrelated board early Tuesday, Redd said she'd like to see Davis and Martinez Jr. on the board.
"We just want to make sure that we have, you know, a good fit in terms of the authority commissioners that serve," Redd said.
For months the authority had trouble reaching a quorum after one commissioner resigned and Jordan's term expired.
Things became more complicated after it came to light that Alamo was a clerk with the city's finance department - forbidden under state law - and the council voted to remove him.