Most of the studies on small area estimation (SAE) focused on the quantitative, count, and categorical variables. However, in practical policy making problems we also require information on class-specific proportions of an ordinal response variable in small areas. This study proposed a model-based approach for estimating class-specific proportions in small areas using unit level cumulative linked mixed models (CLMMs). The CLMMs based SAE method captures the ordering structure of the categories as well as the nested structure of the data to capture between area variability. The suggested CLMMs based method was compared with the direct method using a simulation as well as study on immunization coverage estimation in different districts of Pakistan using Pakistan Demographic and Health Survey (PDHS) 2017-18 data. The CLMM-based SAE methods outperform the direct method in terms of all performance measures used in this study.