DatePicker で日付時刻を入力できる TextField 作った http://miyakeryo.com/?p=457

myoDatePickerField.h

//
//  myoDatePickerField.h
//
//  Created by Miyake Ryo on 13/05/15.
//  Copyright (c) 2013年 Miyake Ryo. All rights reserved.
//

#import <UIKit/UIKit.h>

@protocol myoDatePickerFieldDelegate;

@interface myoDatePickerField : UITextField

@property (nonatomic,weak) id<myoDatePickerFieldDelegate> dpDelegate;
@property (nonatomic,strong) NSDateFormatter *dateFormatter;
@property (nonatomic) NSString        *dateFormat;
@property (nonatomic) NSDate          *date;
@property (nonatomic) NSLocale        *locale;
@property (nonatomic) NSCalendar      *calendar;
@property (nonatomic) NSTimeZone      *timeZone;
@property (nonatomic) UIDatePickerMode datePickerMode;
@property (nonatomic) NSInteger        minuteInterval;
@property (nonatomic) NSDate          *minimumDate;
@property (nonatomic) NSDate          *maximumDate;

- (void)setDate:(NSDate *)date animated:(BOOL)animated;

@end

@protocol myoDatePickerFieldDelegate<NSObject>
@optional
- (void)pickerField:(myoDatePickerField*)pickerField changeDate:(NSDate*)date;
@end

myoDatePickerField.m

//
//  myoDatePickerField.m
//
//  Created by Miyake Ryo on 13/05/15.
//  Copyright (c) 2013年 Miyake Ryo. All rights reserved.
//

#import "myoDatePickerField.h"

@interface myoDatePicker : UIDatePicker
- (void)toggle;
@end

@interface myoDatePickerField ()
@property (nonatomic,strong) myoDatePicker *datePicker;
@end

#pragma mark - myoDatePickerField

@implementation myoDatePickerField

#pragma mark - life cycle

- (id)initWithFrame:(CGRect)frame
{
    self = [super initWithFrame:frame];
    if (self) {
        self.borderStyle = UITextBorderStyleRoundedRect;
        self.contentVerticalAlignment = UIControlContentVerticalAlignmentCenter;
        myoDatePicker *datePicker = [[myoDatePicker alloc] init];
        datePicker.datePickerMode = UIDatePickerModeDateAndTime;
        datePicker.minuteInterval = 1;
        datePicker.minimumDate = [NSDate date];
        datePicker.date = datePicker.minimumDate;
        datePicker.hidden = YES;
        datePicker.autoresizingMask = UIViewAutoresizingFlexibleWidth|UIViewAutoresizingFlexibleTopMargin;
        [datePicker addTarget:self action:@selector(dateChanged:) forControlEvents:UIControlEventValueChanged];
        self.datePicker = datePicker;
    }
    return self;
}

- (void)didMoveToSuperview
{
    [self dateChanged:self.datePicker];
}

- (void)free
{
    [self.datePicker removeFromSuperview];
    self.datePicker = nil;
    self.dateFormatter = nil;
}

- (void)dealloc
{
    [self free];
}

#pragma mark - events

- (BOOL)canBecomeFirstResponder
{
	return YES;
}

- (BOOL)becomeFirstResponder
{
    if(!self.datePicker.hidden)
        return YES;
    UIWindow *window = [[UIApplication sharedApplication] keyWindow];
    CGRect rect = window.bounds;
    rect.origin.y += rect.size.height;
    self.datePicker.frame = rect;
    [window addSubview:self.datePicker];
    [self.datePicker toggle];
    [self.datePicker becomeFirstResponder];
    return YES;
}

- (BOOL)resignFirstResponder
{
    [self.datePicker resignFirstResponder];
    return [super resignFirstResponder];
}

- (void)dateChanged:(UIDatePicker*)datePicker
{
    if(self.dateFormatter){
        self.text =  [self.dateFormatter stringFromDate:datePicker.date];
    }else{
        self.text =  [NSDateFormatter localizedStringFromDate:datePicker.date
                                                    dateStyle:NSDateFormatterShortStyle
                                                    timeStyle:NSDateFormatterShortStyle];
    }
    if([self.dpDelegate respondsToSelector:@selector(pickerField:changeDate:)]){
        [self.dpDelegate pickerField:self changeDate:datePicker.date];
    }
}

#pragma mark - setter methods

- (void)setDateFormat:(NSString*)dateFormat
{
    if(!self.dateFormatter)
        self.dateFormatter = [[NSDateFormatter alloc] init];
    self.dateFormatter.dateFormat = dateFormat;
}
- (void)setDate:(NSDate*)date
{
    [self setDate:date animated:NO];
}
- (void)setDate:(NSDate *)date animated:(BOOL)animated
{
    [self.datePicker setDate:date animated:animated];
    [self dateChanged:self.datePicker];
}
- (void)setLocale:(NSLocale*)locale
{
    self.datePicker.locale = locale;
}
- (void)setCalender:(NSCalendar*)calendar
{
    self.datePicker.calendar = calendar;
}
- (void)setTimeZone:(NSTimeZone*)timeZone
{
    self.datePicker.timeZone = timeZone;
}
- (void)setDatePickerMode:(UIDatePickerMode)datePickerMode
{
    self.datePicker.datePickerMode = datePickerMode;
}
- (void)setMinuteInterval:(NSInteger)minuteInterval
{
    self.datePicker.minuteInterval = minuteInterval;
}
- (void)setMaximumDate:(NSDate*)maximumDate
{
    self.datePicker.maximumDate = maximumDate;
}
- (void)setMinimumDate:(NSDate*)minimumDate
{
    self.datePicker.minimumDate = minimumDate;
}

#pragma mark - getter methods

- (NSDate*)date
{
    return self.datePicker.date;
}
- (NSString*)dateFormat
{
    return self.dateFormatter.dateFormat;
}
- (NSLocale*)locale
{
    return self.datePicker.locale;
}
- (NSCalendar*)calendar
{
    return self.datePicker.calendar;
}
- (NSTimeZone*)timeZone
{
    return self.datePicker.timeZone;
}
- (UIDatePickerMode)datePickerMode
{
    return self.datePicker.datePickerMode;
}
- (NSInteger)minuteInterval
{
    return self.datePicker.minuteInterval;
}
- (NSDate*)maximumDate
{
    return self.datePicker.maximumDate;
}
- (NSDate*)minimumDate
{
    return self.datePicker.minimumDate;
}

@end

#pragma mark - myoDatePicker

@implementation myoDatePicker

- (BOOL)resignFirstResponder
{
    if(!self.hidden)
        [self toggle];
	return [super resignFirstResponder];
}

- (BOOL)canBecomeFirstResponder
{
    return YES;
}

- (void)toggle
{
    typeof(self) __weak _wself = self;
    if(self.hidden){
        self.hidden = NO;
        [UIView animateWithDuration:0.3
                              delay:0.0
                            options:UIViewAnimationOptionCurveEaseInOut
                         animations:^{
                             CGRect rect = _wself.frame;
                             rect.origin.y -= rect.size.height;
                             _wself.frame = rect;
                         }
                         completion:NULL
         ];
    }else{
        [UIView animateWithDuration:0.2
                              delay:0.0
                            options:UIViewAnimationOptionCurveEaseInOut
                         animations:^{
                             CGRect rect = _wself.frame;
                             rect.origin.y += rect.size.height;
                             _wself.frame = rect;
                         }
                         completion:^(BOOL finished){
                             _wself.hidden = YES;
                             [_wself removeFromSuperview];
                         }
         ];
    }
}

@end

ViewController.m

// 使い方

#import "ViewController.h"
#import "myoDatePickerField.h"

@implementation ViewController

- (void)viewDidLoad
{
    [super viewDidLoad];

    myoDatePickerField *timeField;
    timeField = [[myoDatePickerField alloc] initWithFrame:CGRectMake(80,100,160,30)];
    [timeField setDateFormat:@"yyyy/MM/dd HH:mm"];
    [self.view addSubview:timeField];
    
}

@end

ちょっと申し上げにくいですが (^^ ;
実はUIResponderの各サブクラスにはinputViewというプロパティがありまして、これにUIDatePickerを入れてあげるとテキストフィールドをタップしたときにキーボードの代わりにデイトピッカーが表示されるようにできます。