Coyle, who headed West Valley City's now-defunct neighborhood narcotics unit, was demoted to a rank-and-file officer for deficient supervision.
The commission overturned the decision, reinstating Coyle as a lieutenant and awarding him back pay.
"By doing what you're attempting to do at this point in time, it's looking like the city is running and hiding from that decision," Stoney told council members Tuesday.
He said the commission, which Stoney helped found in the early 1980s, has fulfilled its role successfully for more than 30 years.
Cowley, who served under Coyle in the narcotics unit, was fired for mishandling evidence.
His case before the commission was scheduled for a hearing next month.
Cowley also faces separate charges in the Nov. 2, 2012, death of Willard during the course of a drug investigation.
Councilman Steve Buhler voted in favor of disbanding the Civil Service Commission and said "there will always be cases in the pipeline" similar to Cowley's. He hopes a hearing officer can expedite cases and present more definitive decisions, as well as save some money.
"This provision gives me no pause at all," Buhler said.
West Valley City Mayor Ron Bigelow was, however, more hesitant to disband the commission. He voted against the resolution, calling it "abrupt."
"The city may have been talking about it since 2011," the first-term mayor said. "But until I saw it on the agenda last week, I had no idea there was an issue or concern."
Bigelow was unable to attend the study session last week where the resolution was discussed, but West Valley City Attorney Eric Bunderson said the issue has come up previously.
The Civil Service Commission is composed of three citizens hired by the city manager to conduct human-resource functions for West Valley City, as well as hear what Bunderson referred to as "rare" appeals by police and firefighters.
He believes the current process is too time consuming, saying a hearing officer appointed to replace the commission will be able to hear all appeals and act quickly.
The motion to create a hearing officer position was passed with the understanding that the current job description will be reworked.
Councilman Corey Rushton wants to add a term limit to ensure sufficient checks and balances.
Rushton also suggested creating a selection committee that includes citizens to hire the hearing officer, rather than leaving that responsibility solely to the city manager.
But Councilman Tom Huynh, who voted against dissolving the commission, believes those measures aren't enough.
He said the purpose of the commission was to give citizens a voice in the appeals process.
"I believe we have been campaigning pretty big and loud that we want our citizens involved in our city," he said.
"I want to keep people involved in this process."
Bigelow agreed with Huynh, arguing to keep "the common man" involved and to avoid bias by the one-person hearing officer.
The city's seven-member Professional Standards Review Board is also staffed by citizens and hears cases on hiring and firing that involve the police department.
The four council members who voted in favor of disbanding the commission cited this board as a place where citizens can still participate in the city's appeals.
The process to hire the hearing officer will take about a month to complete.
Nicole Cottle, assistant city manager, said it's best to move the hiring process along as quickly as possible.