Can I own a black powder pistol if convicted of a federal felony in Tucson AZ?

No, convicted felons are not lawfully permitted to possess a firearm in any 50 states and U.S. territories. You may seek to have your charge expunged or sealed if it's expungement eligible and if your felony is non-violent you may seek to have, what is known as "restoration of civil rights" motion filed with the court of appeals.