"This Saturday is September ninth."
～月【がつ】counter/name of months
～日【か】counter for days (date)
more about days and months pronunciations here:
That is one possible way to translate it, albeit not very natural sounding in English. の does not directly translate to the possessive *'s format, but it can be translated that way.
'Saturday of this week', 'Saturday this week', and by extension 'This Saturday' are all more natural and valid translations.
川のように is normally translated as 'like a river', not 'like of a river', or 'like a river's ___', even though it has の in it. But, it could also be translated as 'with the appearance of a river' if you wanted to do a more literal translation.
It all boils down to your understanding of the possessive marker and its function, as well as your ability to translate it effectively and naturally in the target language.