Count data from surveys, such as the American Community Survey (ACS), often exhibits more variability than the standard Poisson distribution and as an alternative they can be modeled as a generalized Poisson distribution (Consul and Jain, 1973). If the total is constrained between two categories then the binomial distribution is a natural choice as it is the conditional distribution on the sum of two Poisson random variables. The analog for the generalized Poisson distribution is the quasi-binomial distribution of type II (QBD-II) (Consul, 1975). QBD-II has an additional parameter which serves as a control for overdispersion. A small area model using QBD-II is applied to estimating poverty rates for the Small Area Poverty and Income Estimates (SAPIE) program. A beta distribution regression forms a linking model with the small areas. Small area predictions and formulations are formulated through Bayesian procedures.