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Convolutional Neural Networks (CNNs) are fundamental machine learning tools to process image, speech, or audio signal inputs. The convolutional layer is the core building block of a CNN, and it is where most of the computation occurs. Here, we propose an integrated photonic convolutional accelerator based on time-spatial interleaving utilizing standard generic building blocks to reduce hardware complexity. The architecture is suitable for addressing both 2D and 1D convolutional kernels enabling scalability to more complex networks. Furthermore, a numerical simulation demonstrates the viability of a supervised online learning algorithm for loading the kernel weights both in amplitude and in phase taking in consideration fabrication tolerances and thermal cross-talk.