Не скрывайте панель вкладок и попробуйте следующий код
actionSheet=[[UIActionSheet alloc] init];
[actionSheet showInView:self.tabBarController.tabBar];
actionSheet.frame=CGRectMake(0, 100,480 ,232);
actionSheet.delegate=self;
picker=[[UIPickerView alloc] initWithFrame:CGRectMake(0, 50,480 ,175)];
picker.delegate=self;
picker.showsSelectionIndicator=YES;
[actionSheet addSubview:picker];
UIToolbar *toolbar=[[UIToolbar alloc] initWithFrame:CGRectMake(0, 0,480 ,50)];
toolbar.barStyle =UIBarStyleBlackTranslucent;
NSMutableArray *ButtonArray=[[NSMutableArray alloc ]init];
Save=[[UIBarButtonItem alloc ]initWithTitle:@"Done" style:UIBarButtonItemStyleBordered target:self action:@selector(save_pressed)];
UIBarButtonItem *titleName;
titleName=[[UIBarButtonItem alloc ] initWithTitle: @"Select Date" style:UIBarButtonItemStylePlain target:nil action:nil];
UIBarButtonItem *space=[[UIBarButtonItem alloc] initWithBarButtonSystemItem:UIBarButtonSystemItemFlexibleSpace target:nil action:nil];
UIBarButtonItem *cancel=[[UIBarButtonItem alloc ]initWithTitle:@"Cancel" style:UIBarButtonItemStyleBordered target:self action:@selector(cancel_pressed)];
[ButtonArray addObject:cancel];
[cancel release];
[ButtonArray addObject:space];
[ButtonArray addObject:titleName];
[titleName release];
[ButtonArray addObject:space];
[space release];
[ButtonArray addObject:Save];
[Save release];
[toolbar setItems:ButtonArray];
[ButtonArray release];
[actionSheet addSubview:toolbar];
[toolbar release];
[actionSheet release];