As reported by Sky News and BBC, Coote admitted a charge of making an indecent image of a child in relation to the category A video, the most serious kind, at Nottingham Crown Court in October.
The former referee was sacked in December 2024 after a controversial video surfaced showing him making comments about German football manager Jurgen Klopp.
Judge Nirmal Shant KC told the former referee: "You have had a spectacular fall from grace. Those who commit this sort of offence must understand that they involve real children being abused, with all the consequent damage that comes from it."
She also added that videos such as the one Coote had downloaded "involve a real child being abused”.
Jeremy Janes, prosecuting, said: “He had been filmed making comments about Jürgen Klopp – those comments went viral and put him into the spotlight.
“There was a wider interest and investigation into his conduct by various tabloid newspapers.”
The BBC add that in addition to the suspended prison sentence and sexual harm prevention order, Coote was ordered to carry out 150 hours of unpaid work.
Judge Shant spoke on the order in further detail: "If you breach this order in any way, if there are any further offences - particularly sexual offences - you will be subject to being brought back to court."