Count time series data are frequent in many applied disciplines. In describing them, a specific count may reveal more often than usual. In faming a modeling approach, one must account for the excess count. In this paper, we develop a copula-based time series model for zero-inflated counts with the presence of covariates. Zero-inflated Poisson (ZIP), zero-inflated negative Binomial (ZINB), and zero-inflated Conway-Maxwell-Poisson (ZICMP) distributed marginals will be considered, while the joint distribution is modeled under Gaussian copula with autoregression moving average (ARMA) errors. Likelihood is formulated for inference, under sequential inference method. A simulated study is conducted, and a practical application in environmental setting is described.