Deep neural networks (DNNs) have been successfully deployed for acoustic modelling in statistical parametric speech synthesis (SPSS) systems. Moreover, DNN-based postfilters (PF) have also been shown to outperform conventional postfilters that are widely used in SPSS systems for increasing the quality of synthesized speech. However, existing DNN-based postfilters are trained with speaker-dependent databases. Given that SPSS systems can rapidly adapt to new speakers from generic models, there is a need for DNN-based postfilters that can adapt to new speakers with minimal adaptation data. Here, we compare DNN-, RNN-, and CNN-based postfilters together with adversarial (GAN) training and cluster-based initialization (CI) for rapid adaptation. Results indicate that the feedforward (FF) DNN, together with GAN and CI, significantly outperforms the other recently proposed postfilters.