How to root a samsung galaxy S3 lite(Samsung S6790)
Are you sure that KingoRoot did not root your device? It is reported as working for the Samsung Galaxy S3 Lite. Please verify with a Root Checker if you have root.

Another known method for that device is DF ROOT (direct download). This app may be in Portuguese, so if it is, here are the instructions in English:


Open DF-ROOT.
Go to "Fazer Root."
Choose "Root."
Now go to "Batal" and close the application.
Open SuperSU, it will ask to update the binary SU, select "Continuar."
Select the "Normal" option and then "OK."


Both were reported working in this XDA thread.