Mixed effect binomial regression models are widely used for analysis of correlated count data in which the response is the result of a series of one of two possible disjoint outcomes. In this paper, we consider kernel extensions with nonparametric fixed effects and parametric random effects. The estimation is through the penalized likelihood method based on kernel trick, and our focus is on the efficient computation and the effective hyperparameter selection. For the selection of hyperparameters, cross-validation techniques are employed. Examples illustrating usage and features of the proposed method are provided.