Hi,
either I did not understand how to use the updateDayText method or it simply never worked.
Here is my override:

Code:
/**
 * @author: Torsten Dinkheller (Mobile Game Design e.K., Germany)
 * 
 * Updates the methods for the dayText, monthText, yearText
 */
Ext.define('App.override.picker.Date', {
    override: 'Ext.picker.Date',


    /**
     * Updates the monthText configuration
     */
    updateMonthText: function(newMonthText, oldMonthText) {
        this.updateDateText(newMonthText, oldMonthText);
    },


    /**
     * Updates the dayText configuraton
     */
    updateDayText: function(newDayText, oldDayText) {
        this.updateDateText(newDayText, oldDayText)
    },


    /**
     * Updates the yearText configuration
     */
    updateYearText: function(newYearText, oldYearText) {
        this.updateDateText(newYearText, oldYearText);
    },


    /**
     * Updates the Text configuration for day, month, year
     */
    updateDateText: function(newText, oldText) {
        var innerItems = this.getInnerItems(),
            ln = innerItems.length,
            item, i;


        //loop through each of the current items and set the title on the correct slice
        if (this.initialized) {
            for (i = 0; i < ln; i++) {
                item = innerItems[i];


                if ((typeof item.getTitle() == "string" && item.getTitle() == oldText) || (item.getTitle().getHtml() == oldText)) {
                    item.setTitle(newText);
                }
            }
        }
    }
});