The bivariate Poisson distribution can be formed with the help of three independent univariate Poisson distributions. We generated values from a bivariate Poisson distribution via simulation and tried to estimate the covariance parameter which is of great importance since the correlation coefficient is linked to it. There are several methods to estimate the parameters of this distribution and hence the correlation coefficient. In this study we provide a comparison of various non parametric methods for estimating the true value of this coefficient. Techniques such as bootstrap-t, BCA, Fisher's approximation and more, are discussed along with their advantages and drawbacks. The Studentized Bootstrap presented a good coverage probability and a tolerable Confidence Interval and Mean Length.