Workaround 1) Use .resx files as the attached ones 

Workaround 2) Set properties to ViewState
        RadMonthYearPicker1.MonthYearNavigationSettings.ViewState["_mCancelButtonCaption"] = "my cancel";
        RadMonthYearPicker1.MonthYearNavigationSettings.ViewState["_mTodayButtonCaption"] = "my today";
        RadMonthYearPicker1.MonthYearNavigationSettings.ViewState["_mOkButtonCaption"] = "my ok";