Really??Some context might help us understand more exactly what nuance of "On any given Sunday" is involved.
Literally, "given" means "gegeben", but chances are you mean an arbitrary Sunday (perhaps in a statistical sense); I think this might work well as "An irgendeinem beliebigen Sonntag".
I am unaware of any such catchphrase that would refer to something that isn't specifically a Sunday, though it may have tangentially acquired that meaning following the 1999 movie of that name, which I hadn't heard of until now. The title of this, by the way, has been translated as An jedem verdammten Sonntag, which does mean "every damned Sunday", but this is just poetic licence (title translations are often completely different from their originals, just look at what The Sound of Music became in German).Really??
I always thought that 'any given Sunday' is just a fixed catchphrase and doesn't really relate to Sundays specifically!?? So, more in the sense of 'any given day' or 'any time/any moment'.