Google translate gives "in eine Weise zu sprechen" but that strikes me as a literal translation that doesn't have the right "ring" to it. Is that, in fact, the best translation or is there a better one?
Two of the possible translation of "manner" are indeed "Art" or "Weise", in German often combined:
In einer Art und Weise
Thus, "in (such) a manner" can be translated with "in einer Weise" or "derart". dict.leo
However, in this example you shouldn't translate it like that. "In a manner of speaking" is a phrase with a particular meaning and thus you need to find the German equivalent of that saying. Some examples how to translate "manner of speaking" are also given by dict.leo. More examples on bab.la.