Ian Ruddock was accused of murdering five-week-old Olivia at his home in Clarkston, East Renfrewshire, in 2011.
But a jury at the High Court in Edinburgh found him guilty of a reduced charge of culpable homicide.
Ruddock was also found guilty of the attempted murder of a baby boy in Glasgow in 2013. Sentence was deferred and he was remanded in custody.
A 34-year-old man has been convicted of killing his infant daughter and attempting to murder a baby boy.