@flaxter has committed the crime of talking about periodic kernels in the last few days, so maybe he can give better comments here, but I’ll try to just provide pointers.
Check out: Approximate GPs with Spectral Stuff
The Stan model at the top has Fourier in the name. Not sure what it is, but anything Fourier seems like it’d be good for periodic stuff. The arxiv paper on the Poisson intensity estimation he links there has another kernel defined on a periodic domain.
I just Googled periodic RBF and this page came up: http://www.cs.toronto.edu/~duvenaud/cookbook/index.html . It has some sorta strange periodic kernel there that might work!