まあまあ、そう怒らないでくださいな。

、。

Now, now — please don't get so worked up.

Literal

Now-now, that-way get-angry-[don't-ないで] [please-ください] [softener-な].

まあまあ here is the interjection for calming someone down ('there, there / now, now') — distinct from its adjectival use meaning 'so-so.' ~ないでください is the polite negative request pattern 'please don't X.' The sentence-final な tacked onto ください is a pleading softener, distinct from the harsh prohibitive な on dictionary forms (compare 怒るな 'don't get angry').