Davis resigned Tuesday without explanation.
Council members met in a closed-door session prior to the meeting.
Several of them also took time at the end of the meeting to shower praise on Davis.
"From my perspective he's always done what he believes to be right for the community," Councilman Chris McConnehey said. "His resignation caught me by complete surprise."
Councilman Chad Nichols said during his three years on the job, Davis improved city finances, morale and transparency.
News reports in recent days detailed controversy over the civil-rights lawsuit brought against Davis and city attorneys by a city justice court clerk supervisor and the disclosure of Davis' longtime employment as a senior executive with an Arizona-based consulting firm on top of his nearly $200,000 city compensation.
But only two members of the public spoke about the matter Wednesday during the council's open-comment period.
One of those: John Geilmann, a former South Jordan city manager, took the opportunity to make his pitch for the job as manager.
Resident Alexandra Eframo, however, said she was "appalled" at Davis' outside consulting work.
"I'm begging you, when you're looking for a new manager: 24/7 I want our manager to focus on our city and not on another firm."