создайте собственный UIDatePicker, который подходит для быстрого назначения встреч

class ViewController: UIViewController , UIPickerViewDelegate, 
UIPickerViewDataSource
{

var pickerView: UIPickerView!

@IBOutlet weak var textField: UITextField!

var arrDate = [String]()

override func viewDidLoad() {
    super.viewDidLoad()

    // Do any additional setup after loading the view.


    arrDate.append(Date().getDateStringWithFormate("yyyy-MM-dd", timezone: TimeZone.current.abbreviation()!))

    for i in 1...7
    {
        let dateAdded = Date().addDays(i)
        arrDate.append(dateAdded.getDateStringWithFormate("yyyy-MM-dd", timezone: TimeZone.current.abbreviation()!))
        print(arrDate)
    }


    pickerView = UIPickerView()
    pickerView.delegate = self
    pickerView.dataSource = self


    let keyboardToolbar = UIToolbar(frame: CGRect(x: 0, y: 0, width: UIScreen.main.bounds.size.width, height: 44))
    keyboardToolbar.barStyle = .black
    keyboardToolbar.tintColor = UIColor.white

    let barButtonItem = UIBarButtonItem(title: NSLocalizedString("Done", comment: ""), style: .done, target: self, action: #selector(clickToKeyboardToolbarDone(sender:)))

    //(barButtonSystemItem: .done, target: self, action: #selector(clickToKeyboardToolbarDone(sender:)))


    let flex = UIBarButtonItem(barButtonSystemItem: .flexibleSpace, target: self, action: nil)

    let items = [flex, barButtonItem]
    keyboardToolbar.setItems(items, animated: true)

    textField.inputAccessoryView = keyboardToolbar
    textField.inputView = pickerView

}

@IBAction func clickToKeyboardToolbarDone(sender: UIBarButtonItem)
{
    if(textField.isFirstResponder)
    {
        let selectedIndex = pickerView.selectedRow(inComponent: 0)
        let currentDate = arrDate[selectedIndex]

        print("currentDate",currentDate)
    }

    textField.resignFirstResponder()

}

//MARK: - UIPickerViewDelegate, UIPickerViewDataSource Methods

func numberOfComponents(in pickerView: UIPickerView) -> Int
{
    return 1
}

func pickerView(_ pickerView: UIPickerView, numberOfRowsInComponent component: Int) -> Int
{
    return arrDate.count
}

func pickerView(_ pickerView: UIPickerView, titleForRow row: Int, forComponent component: Int) -> String?
{
    return arrDate[row]
}

override func didReceiveMemoryWarning() {
    super.didReceiveMemoryWarning()
    // Dispose of any resources that can be recreated.
}


/*
// MARK: - Navigation

// In a storyboard-based application, you will often want to do a little preparation before navigation
override func prepare(for segue: UIStoryboardSegue, sender: Any?) {
    // Get the new view controller using segue.destinationViewController.
    // Pass the selected object to the new view controller.
}
*/

}



//MARK: - All Date Extension
extension Date
{
   func getDateStringWithFormate(_ formate: String, timezone: String) -> String
    {
        let formatter = DateFormatter()
    formatter.dateFormat = formate
    formatter.timeZone = TimeZone(abbreviation: timezone)

    return formatter.string(from: self)
    }
}

Вы можете использовать представление custompicker, создать массив дат на сегодняшний день до 7 дней, попробуйте этот код.