Convolutional Neural Networks (ConvNets) are a powerful Deep Learning model, providing state-of-the-art accuracy to many emerging classification problems. However, ConvNet classification is a computationally heavy task, suffering from rapid complexity scaling. This paper presents fpgaConvNet, a novel domain-specific modelling framework together with an automated design methodology for the mapping of ConvNets onto reconfigurable FPGA-based platforms. By interpreting ConvNet classification as a streaming application, the proposed framework employs the Synchronous Dataflow (SDF) model of computation as its basis and proposes a set of transformations on the SDF graph that explore the performance-resource design space, while taking into account platform-specific resource constraints. A comparison with existing ConvNet FPGA works shows that the proposed fully-automated methodology yields hardware designs that improve the performance density by up to 1.62× and reach up to 90.75% of the raw performance of architectures that are hand-tuned for particular ConvNets.