In this work we propose a new methodology for neural network hardware implementation based on an efficient combination of Stochastic Computing and Morphological Neural Networks (MNN). The main reasons behind the use of morphological neurons instead of conventional ones are that activation functions are not used and that Stochastic Computing can be adapted to implement MNN in a natural and compact way. The proposed design methodology has been verified by implementing classical pattern recognition problems such as Fisher\'s IRIS dataset or handwritten digit recognition problems. As a result, the proposed design is able to provide competitive accuracy results along with higher energy efficiency and hardware compactness if compared to other alternatives.