Recurrent neural network language models (RNNLMs) have been shown to consistently improve Word Error Rates (WERs) of large vocabulary speech recognition systems employing n-gram LMs. In this paper we investigate supervised and unsupervised discriminative adaptation of RNNLMs in a broadcast transcription task to target domains defined by either genre or show. We have explored two approaches based on (1) scaling forward-propagated hidden activations (Learning Hidden Unit Contributions (LHUC) technique) and (2) direct fine-tuning of the parameters of the whole RNNLM. To investigate the effectiveness of the proposed methods we carry out experiments on multi-genre broadcast (MGB) data following the MGB-2015 challenge protocol. We observe small but significant improvements in WER compared to a strong unadapted RNNLM model.