Ah, stara. Finally, A Clockwork Orange's Nadsat has helped me guess the meaning of a new word without having to check the hints.
It is an odd expression, no doubt put together to illustrate specific words or word endings, but what would "Fresh tea and stale coffee" be?
'świeża herbata' for sure but about the coffee... I don't know, I don't drink coffee so I don't know the right word. Maybe simply 'nieświeża'? Actually, I can imagine 'stara'...
I think the word you are searching for might be „odstana”, but careful now though, it might be Małopolan dialect ;P – there is a metric ton of results in google(especially with beer), but adjective „odstany” isn't in any dictionary I checked…
Still, that's definitely what I would have used. ;)