Circuit:

[RTS] o---.
          |
          o |
            |=| Push switch
          o |
          |
[CTS] o---+
          |
         | |
         | | 10K
         |_|
          |
[GND] o---'

Code:

using System;
using System.IO.Ports;
using System.Media;

namespace Doorbell {
    class Program {
        static void Main(string[] args) {
            
            using (var Port = new SerialPort("COM1")) {
                bool OldPinState = false;

                Port.PinChanged += (sender, e) => {
                    if (e.EventType == SerialPinChange.CtsChanged) {
                        var NewPinState = Port.CtsHolding;
                        if (NewPinState && !OldPinState) {
                            SystemSounds.Beep.Play();
                        }
                        OldPinState = NewPinState;
                    }
                };

                Port.Open();
                Port.RtsEnable = true;

                Console.WriteLine("Press any key to exit.");
                Console.ReadKey(true);
            }
        }
    }
}