I have a database.php. I want to keep it in my github repository without any sensitive information.
First I pushed to my repository without any sensitive info.
You should use a filter driver able to:

smudge script, detect the content (those 'filter driver' scripts don't have the name of the files they are filtering) of a database.templatedatabase.php, based on the values of a:
database.private.value file (also always ignored)database.private.value isn't found (which is the case for your user cloning your repo), a database.public.value file (which is pushed to the remote repo)clean) step.