He was accused of organising the 2007 burning of two cars outside the south Dublin home of Nurse Officer Orla Finn from his cell in Wheatfield Prison, where he was serving a sentence for public order offences.
Ryan, of Ballygarett, Gorey had pleaded not guilty at Dublin Circuit Criminal Court.
The jury of four men and eight women unanimously found him not guilty of the two counts of arson.
On Monday, Judge Patrick McCartan directed the jury to find Ryan not guilty of using a mobile phone from prison after ruling that there wasn't enough evidence to support this charge.
The jury had heard that two days before alleged arson attack Ryan had repeatedly asked prison officers for a cream to treat haemorrhoids.
Nurse Finn said she handed him a sealed box of Anusol cream from a locked prison pharmacy. She said that Ryan was aggressive and told her, 'I hope you get cancer and die'.
She made an official complaint to the prison governor, Seamus Creamer, and Ryan was put on disciplinary report.
Ryan told Mr Creamer that the nurse had given him a packet of Ambre Solaire sun cream inside the Anusol box.
Ryan then handed him the Anusol box, an applicator and a small packet of Ambre Solaire.
Mr Creamer said that Ryan told him he knew where the nurse lived because he used to be a neighbour of hers.
During recorded calls from prison, Ryan told his wife, Fiona, "I want something done".
After his arrest Ryan told gardai that he wanted someone to "have a word with" Ms Finn.
The fire at Ms Finn's house destroyed both her car and her mother's Nissan Micra, and the front of their home was damaged by smoke. Ms Finn said she was left terrified in her own home after the alleged attack.