Electronic beehive monitoring extracts critical information on colony behavior and phenology without invasive beehive inspections and transportation costs. As an integral component of electronic beehive monitoring, audio beehive monitoring has the potential to automate the identification of various stressors for honeybee colonies from beehive audio samples. In this investigation, we designed several convolutional neural networks and compared their performance with four standard machine learning methods (logistic regression, k-nearest neighbors, support vector machines, and random forests) in classifying audio samples from microphones deployed above landing pads of Langstroth beehives. On a dataset of 10,260 audio samples where the training and testing samples were separated from the validation samples by beehive and location, a shallower raw audio convolutional neural network with a custom layer outperformed three deeper raw audio convolutional neural networks without custom layers and performed on par with the four machine learning methods trained to classify feature vectors extracted from raw audio samples. On a more challenging dataset of 12,914 audio samples where the training and testing samples were separated from the validation samples by beehive, location, time, and bee race, all raw audio convolutional neural networks performed better than the four machine learning methods and a convolutional neural network trained to classify spectrogram images of audio samples. A trained raw audio convolutional neural network was successfully tested in situ on a low voltage Raspberry Pi computer, which indicates that convolutional neural networks can be added to a repertoire of in situ audio classification algorithms for electronic beehive monitoring. The main trade-off between deep learning and standard machine learning is between feature engineering and training time: while the convolutional neural networks required no feature engineering and generalized better on the second, more challenging dataset, they took considerably more time to train than the machine learning methods. To ensure the replicability of our findings and to provide performance benchmarks for interested research and citizen science communities, we have made public our source code and our curated datasets.