It is known that some particular neurons in our brains produce various periodic patterns, such as locomotion, heart rhythm and so on. We have already proposed a method to synthesize spiking neural oscillators which generate periodic spike trains in spiking neural networks.In applying neural oscillators to engineering problems, their stability often become an important issue. Thus, we have proposed a method to analyze stability of periodic spike trains. In this paper, we propose a learning method to synthesize spiking neural oscillators with considering their stability.