We recently proposed the STiDi-BP algorithm, which avoids backward recursive gradient computation, for training multi-layer spiking neural networks (SNNs) with single-spike-based temporal coding. The algorithm employs a linear approximation to compute the derivative of the spike latency with respect to the membrane potential and it uses spiking neurons with piecewise linear postsynaptic potential to reduce the computational cost and the complexity of neural processing. In this paper, we extend the STiDi-BP algorithm to employ it in deeper and convolutional architectures. The evaluation results on the image classification task based on two popular benchmarks, MNIST and Fashion-MNIST datasets with the accuracies of respectively 99.2% and 92.8%, confirm that this algorithm has been applicable in deep SNNs. Another issue we consider is the reduction of memory storage and computational cost. To do so, we consider a convolutional SNN (CSNN) with two sets of weights: real-valued weights that are updated in the backward pass and their signs, binary weights, that are employed in the feedforward process. We evaluate the binary CSNN on two datasets of MNIST and Fashion-MNIST and obtain acceptable performance with a negligible accuracy drop with respect to real-valued weights (about $0.6%$ and $0.8%$ drops, respectively).