We analyse, in a systematic way, four-dimensional Einstein - Weyl spaces equipped with a diagonal Kähler Bianchi IX metric. In particular, we show that the subclass of Einstein - Weyl structures with a constant conformal scalar curvature is the one with a conformally scalar flat - but not necessarily scalar flat - metric; we exhibit its three-parameter distance and Weyl 1-form. This extends the previous analysis of Pedersen, Swann and Madsen, limited to the scalar flat, antiself-dual case. We also check, in agreement with a theorem of Derdzinski, that the most general conformally Einstein metric in the family of biaxial Kähler Bianchi IX metrics is an extremal metric of Calabi, conformal to Carter's metric, thanks to Chave and Valent's results.