The error diffusion method can effectively reduce quality degradation by propagating thresholding errors to neighboring pixels in the conversion of a gray-scale hologram to a binary hologram. In previous works, the four weighting coefficients in error diffusion are mostly set as the Floyd-Steinberg coefficient, which was determined empirically and originally proposed for photograph processing. In this work, we point out that the Floyd-Steinberg coefficients can be suboptimal for hologram error diffusion binarization. Furthermore, the weighting coefficients are optimized for each different hologram adaptively. Compared with conventional coefficients, our optimized coefficients can better preserve the fidelity of a reconstructed image after a hologram is binarized.