They held a press conference at Dallas City Hall Tuesday to issue their demands to police.
"We are for good law enforcement, but we also want the fair and equitable administration of justice," said LULAC leader Jesse Garcia.
In both cases police said at the time the suspects had been combative and police had reason to believe they posed a threat.
Both suspects had prior criminal records.
Early Sunday, Nov. 7, police said suspect Tony Menchaca, 32, had repeatedly told officers he had a gun and planned to shoot them with it during a stand off on Davis Street.
He was shot when he reached for the place on his waist where the said the gun was hidden.
Menchaca was shot about two dozen times by five different officers.
On Friday, Oct. 29, police said Tobias Mackey, 25, was shot when he made a sudden move after defying police commands.
"We are not pleased with the tragedies of our people," said Dallas NAACP President Juanita Wallace. "We demand changes to the deadly force practices."
The group wants better training for officers, new community relations efforts from the department and plans a series of community meetings to be attended by police officials.
Coalition leaders said Dallas Police Chief David Brown has promised to attend.
Several of the leaders say they strongly support the chief but want him to make changes that will ease community concerns.
"I know that many are working to riot. I understand that many are wanting to rally. But I would strongly recommend and extend the opportunity for us to come to the table as a community," said Kellie Obazee with the Dallas Peace Center.
A police spokesman declined to comment directly on the demands but said that internal affairs investigations of officer conduct in the two shootings are still pending.