We develop biologically plausible training mechanisms for self-supervised learning (SSL) in deep networks. SSL, with a contrastive loss, is more natural as it does not require labelled data and its robustness to perturbations yields more adaptable embeddings. Moreover the perturbation of data required to create positive pairs for SSL is easily produced in a natural environment by observing objects in motion and with variable lighting over time. We propose a contrastive hinge based loss whose error involves simple local computations as opposed to the standard contrastive losses employed in the literature, which do not lend themselves easily to implementation in a network architecture due to complex computations involving ratios and inner products. Furthermore we show that learning can be performed with one of two more plausible alternatives to backpropagation. The first is difference target propagation (DTP), which trains network parameters using target-based local losses and employs a Hebbian learning rule, thus overcoming the biologically implausible symmetric weight problem in backpropagation. The second is simply layer-wise learning, where each layer is directly connected to a layer computing the loss error. The layers are either updated sequentially in a greedy fashion (GLL) or in random order (RLL), and each training stage involves a single hidden layer network. The one step backpropagation needed for each such network can either be altered with fixed random feedback weights as proposed in Lillicrap et al. (2016), or using updated random feedback as in Amit (2019). Both methods represent alternatives to the symmetric weight issue of backpropagation. By training convolutional neural networks (CNNs) with SSL and DTP, GLL or RLL, we find that our proposed framework achieves comparable performance to its implausible counterparts in both linear evaluation and transfer learning tasks.