Biological and medical research often collect count data in clusters at multiple time points. The data may also exhibit excessive zeroes and uncertainty in levels of dispersion. We propose a novel longitudinal approach of marginal regression based on zero-inflated Conway-Maxwell-Poisson (ZICMP) distribution to analyze these data features. Two methods are introduced to estimate parameters for the longitudinal marginal models: one uses the estimation-solution algorithm; the other maximizes the pseudo likelihood function. Additionally, we study the bootstrap variance and the resulting confidence intervals through simulation. Further exploration on spatial temporal covariance structures are also incorporated in our longitudinal ZICMP model. We apply the models to analyze the caries experience scores of children at the age of 5, 9, and 13 from the Iowa Fluoride Study, which was originally designed to associate the longitudinal fluoride exposure from both dietary and non-dietary sources with dental fluorosis (spots on teeth) and dental caries (cavities).