Obtaining data to train robust artificial intelligence (AI)-based models for species classification can be challenging, particularly for rare species. Data augmentation can boost classification accuracy by increasing the diversity of training data and is cheaper to obtain than expert-labelled data. However, many classic image-based augmentation techniques are not suitable for audio spectrograms. We investigate two generative AI models as data augmentation tools to synthesise spectrograms and supplement audio data: Auxiliary Classifier Generative Adversarial Networks (ACGAN) and Denoising Diffusion Probabilistic Models (DDPMs). The latter performed particularly well in terms of both realism of generated spectrograms and accuracy in a resulting classification task. Alongside these new approaches, we present a new audio data set of 640 hours of bird calls from wind farm sites in Ireland, approximately 800 samples of which have been labelled by experts. Wind farm data are particularly challenging for classification models given the background wind and turbine noise. Training an ensemble of classification models on real and synthetic data combined compared well with highly confident BirdNET predictions. Each classifier we used was improved by including synthetic data, and classification metrics generally improved in line with the amount of synthetic data added. Our approach can be used to augment acoustic signals for more species and other land-use types, and has the potential to bring about advances in our capacity to develop reliable AI-based detection of rare species. Our code is available at https://github.com/gibbona1/SpectrogramGenAI.