This paper presents a deep learning based approach for small-signal stability of a single machine connected to infinite bus. The proposed approach is based on an optimal estimation of the synchronizing and damping torque coefficients of the synchronous generator by optimal measurement of the operating conditions including the voltage, real power and reactive power. The proposed approach in this paper is to train deep neural networks to estimate the synchronizing and damping torque coefficients for all examples that the power system may encounter. Hence, a large dataset of more than 310,000 examples is created to cover the full range of the possible operation conditions. The performance of deep neural networks based approach is compared with that of other neural networks reported in the literature. Simulations results show that the proposed approach is robust and training the neural network over a wide range of operating conditions yield fast, yet accurate estimation of the torque coefficients.