In spatial epidemiology and public health studies, including covariates in small area estimation of spatial binary data remains a challenge. In this paper, Moran's spatial filtering is proposed to model two-scale spatial binary data. Two models are developed: the first uses deterministic estimation of the sample size at small areal level; the second generates a random sample size using the multinomial distribution. The models were applied to estimate the underweight among children at Vietnamese district level using sampling survey data at provincial level. The results show that the first model outperformed the second model regarding its accuracy and simplicity. Eigenvector maps improve model parameter estimation, and allow for the effects of spatial spillover and covariates. Prediction at the district level indicates that many underweight children came from the mountainous areas in 2014. The study concludes that the proposed models serve as alternatives to small area estimation of spatial binary data.