Translation:I cannot run with a cup of coffee.
Coffee cup = kaffekopp, i.e. a cup used for coffee. "En kopp kaffe" = "a cup of coffee", i.e. coffee contained in a cup.
A coffee cup = en kaffekopp, while a cup of coffee is "en kopp kaffe". Similarly you have "et vinglass" and "et glass vin" and " en tekopp" and "en kopp te".
That wouldn't sound natural in English, as 'a' is often used as a generic, rather than specific, singular. It's a hard concept to explain, but essentially 'I can't run with one cup of coffee" would only really sound normal in reference or reply to a discussing someone that was hypothetically running with several cups of coffee.
Because the coffee always chooses to work out at the gym (it's all that caffeine).