Justices Wanjiru Karanja, Kathurima M’inoti and Jamilla Mohamed dismissed Mberia's application saying it lacked merit.
Mberia had asked the appellate court to issue an interim relief pending a hearing and determination of his criminal appeal which is currently before the High Court.
His main prayer was that the court suspends implementation of the sentence and order made on February 25 barring him from serving as a member of the Nairobi county assembly.
Mberia was in February last year convicted for receiving a Sh1.7 million bribe.
He was sentenced to three years in jail or an alternative fine of Sh700,000. He chose to pay the fine.
But being aggrieved, he lodged a criminal appeal which is still pending a hearing and determination at the High Court.
The magistrate court also barred him from holding public office as an MCA.
The Court of Appeal judges on Tuesday observed that although the appeal was ready for hearing, Mberia declined to prosecute it
He urged the High Court to hear his application to suspend part of the sentence delivered in February last year.
That the application was dismissed by the High Court and he then moved to the appellate court.
The judges of the Court of Appeal said the record shows his appeal in the High Court was ready for hearing in March 2021.
But Mberia refused to prosecute the appeal to create a false ground to argue that his seat cannot be declared vacant because of the pending appeal.
"We cannot grant orders sought because of his own conduct which is calculated to undermine core constitutional principles under the guise of defending and upholding the constitution," the judges said.
(Edited by Tabnacha O)