A jury at the High Court in Livingston returned a majority verdict finding Iain Murray guilty of sexually assaulting the youngster over five and a half years.
The jury found allegations that he raped his victim and sexually assaulted her eight year-old sister not proven.
Murray was cleared of three charges of sexually assaulting and attempting to rape the girls’ mother, now aged 30, more than 15 years ago.
The jury heard evidence that the matter was reported to the police in 2003 but he was not prosecuted then because of lack of evidence.
The Crown alleged that the series of six offences – all of which Murray denied – were committed either at his then home in Bannockburn, Stirlingshire, or at an address near Falkirk.
Police launched an investigation after the 12-year-old’s mum found an entry in her daughter’s diary saying that Murray was “a paedo”.
She confronted the accused, who denied doing anything to the girls who she had entrusted to his care.
Judge Lord Burns placed Murray on the sex offenders’ register and told him details of his conviction would be notified to Scottish Ministers under protection of vulnerable groups legislation.
He called for social work background reports and told the first offender that he should attend for sentence at the High Court in Aberdeen on June 22.
He continued Murray’s bail with special conditions not to contact the complainers in the case.
He warned Murray: “I have not ruled out any sentencing option that is before me.
“You should not take the fact that I’ve continued your bail in any way as informing you that a custodial sentence will not be imposed.”