Would you like to meet for coffee?

Shall we meet for coffee?

Or, depending on the situation, maybe something like "What do you think about getting together over a coffee?"

D'you fancy going for a coffee?

Very informal UK English. Perhaps too informal. IF so, Debbie's version sounds right.

By the way, the word 'fancy' is quite useful. Here it means 'would you like to ...'. Similarly you might say 'I fancy a chocolate muffin' or 'I fancy that bloke in the Accounts Department'.

Hallo Ihr Lieben, vielen Dank für eure Vorschläge!