Brian McKerrow, 42, threatened SNP politician Christina McKelvie by phone and in person at the politician's constituency offices in Hamilton.
He also made threats in person and by phone to Samantha Poling at the BBC offices in Pacific Quay, Glasgow, where the Panorama journalist is based.
The repeated threats against both women are said to have been made between May of last year and June this year.
McKerrow, of Larkhall, Lanarkshire, had been on trial at Hamilton Sheriff Court since November and had been defending himself.
The court heard Ms McKelvie, 46, say McKerrow had threatened to "take up arms" against her if she would not take on his case.
The pair first met while the MSP was out campaigning in Hamilton during the 2011 Holyrood elections. McKerrow asked for Ms McKelvie's assistance in getting access to his children.
However, he launched into rants against Ms McKelvie and her office staff when he was told she could not help.
The MSP told the court she was so concerned for her safety she bought a dog.
She said: "I have never been as unnerved as I have been with Mr McKerrow. At one point he told me that he knew people in the military who would sort us out.
"He then demanded a meeting with me which he said would be historic, which put me in a state of fear and alarm."
She added: "He said he would take up arms against me.
"This has made me much more wary. I'm now nervous when I'm in a dark car park or street in case something happens. I even bought myself a dog."
McKerrow also contacted Ms Poling, who had initially shown an interest in making a programme about his campaign for fathers' rights.
However, following a meeting with him, Ms Poling withdrew from the project.
But after enduring nearly a year of calls and contact from McKerrow she reported him to BBC security chiefs in May 2012.
She told the trial she was left terrified after McKerrow told her during one phone call that she was going to be "extinguished".
Ms Poling, who regularly goes undercover with hardened criminals for investigations, added she had never been more frightened than when dealing with McKerrow.
McKerrow denied all the charges against him and lodged a list of witnesses that included Justice Secretary Kenny MacAskill and MSP Roseanna Cunningham.
However, prosecutors objected to them being called and McKerrow had to rely on his own evidence in his defence.
He was found guilty by Sheriff Vincent Smith and sentence was deferred for background reports.
In an unrelated incident in 2011, Ms Poling was attacked as she filmed a documentary about counterfeit cigarettes at the Barras Market in Glasgow.
Alexander Quinn pleaded guilty to assault and breach of the peace and was fined £300 for that offence.
Ms McKelvie was elected as MSP for Central Scotland in 2007 and then re-elected in 2011 as constituency MSP for Hamilton, Larkhall and Stonehouse.