Как то так.
using System;
using System.Drawing;
using System.Windows.Forms;
namespace RandomButton
{
    public partial class Form1 : Form
    {
        Point templocation = new Point(0, 0);
        Timer timer = new Timer();
        Random rnd = new Random();
        public Form1()
        {
            InitializeComponent();
            timer.Tick += Timer_Tick;
            timer.Interval = 5000;
        }
        private void Timer_Tick(object sender, EventArgs e)
        {
            button1.Location = templocation;
            templocation.X = rnd.Next(10,200);
            button1.Location = templocation;
            templocation.Y = rnd.Next(10,200);
        }
        private void Form1_Load(object sender, EventArgs e)
        {
            timer.Start();
        }
    }
}