There is a growing need for current and reliable counts at small area level. The empirical predictor under a generalised linear mixed model (GLMM) is often used for small area estimation (SAE) of such counts. However, the fixed effect parameters of a GLMM are spatially invariant and do not account for the presence of spatial nonstationarity in the population of interest. A geographically weighted regression extension of the GLMM is developed, extending this model to allow for spatial nonstationarity, and SAE based on this spatially nonstationary model (NSGLMM) is described. The empirical predictor for small area counts (NSEP) under an area level NSGLMM is proposed. Analytic and bootstrap approaches to estimating the mean squared error of the NSEP are also developed, and a parametric approach to testing for spatial nonstationarity is described. The approach is illustrated by applying it to a study of poverty mapping using socio-economic survey data from India.