In this paper, we study the properties of two kinds of SU(1,1) coherent states of light with Bargman index k=1/4 and k=3/4 and show that they posses different quantum statistical properties. The atomic dynamical behavior in a two-photon Jaynes-Cummings model with initial SU(1,1)coherent state field are discussed. We show that the time evolution of atomic inversion displays peculiar periodic oscillation and pulse which are very different from coherent states of light.