Vehicular Ad-hoc Networks (VANETs) are an evolving technology in the transportation industry. Reliability is a critical issues in vehicular communications to ensure road safety. An analytical framework is presented in this paper to estimate the reliability of Vehicle-to-Vehicle (V2V) communications in Cognitive Radio (CR)-VANETs. The proposed framework considers nodes' reliability and different challenges of physical, MAC, and network layers for communications' reliability, including the probability of channel availability for CR-enabled vehicles, channel fading, contention among the transmitting vehicles, hidden terminal problem, and transmission redundancy. The channel availability for reliability assessments of CR vehicular communications has not been considered in the previous research. Therefore, a Markov model is proposed to estimate the probability of channel availability for CR-enabled vehicular nodes. Also, a dataset is created using the proposed analytical framework, and the reliability estimation of the V2V communications is automated using an Artificial Neural Network (ANN) model. The analytical findings are validated by NS-3 simulations and compared with existing methods, showing the accuracy of the proposed method. Moreover, the correlation coefficient (R) and Root Mean Square Error (RMSE) of the test data for the best case of the ANN model, with one hidden layer, are 0.9948 and 0.0289, respectively. These values indicate the accurate estimation of CR-vehicular communications' reliability by the analytical framework.