Mr Justice Tugendhat said 65-year-old Tony Bennett deliberately flouted legal undertakings, given in November 2009, not to repeat allegations about the couple.
He said his conduct was so serious that nothing less than a custodial sentence of three months, suspended for one year, would reflect the harm he had done.
Finding Bennett guilty of contempt of court, the judge added: "I am sure that he intended to allege that the claimants are to be suspected of causing the death of their daughter, and did in fact dispose of her body, lie about what happened and covered up what they had done."
The judge, at London's High Court, said he was satisfied that Bennett, of Harlow, Essex, was in breach of the undertakings in each of the 13 representative instances before the court – out of 153 publications complained of.
Bennett said: "I recognise the distress I have caused on a number of occasions to the claimants. I would like to apologise to them."