RandomScheduler.cs

using System;
using System.Collections.Generic;

namespace RandomScheduler
{
    class Program
    {
        public static Random R = new Random();

        static void Main()
        {
            var now = DateTime.Now;
            var random = new Random((int)now.Ticks);
            const int windowOfHours = 12;
            
            const int numOfEvents = 5;

            // let's start the window 8 AM
            var start = new DateTime(now.Year, now.Month, now.Day, 8, 0, 0, 0);
            // let's end 12 hours later
            var end = start.AddHours(windowOfHours);

            var prev = null as DateTime?;
            const int hoursInEachSection = windowOfHours / numOfEvents;
            double minimumTimeApartInHours = hoursInEachSection / 1.5;

            var events = new List<DateTime>();

            for (var i = 0; i < numOfEvents; i++)
            {
                // if there is a previous value
                // let's at least start 2 hours later
                if (prev.HasValue)
                    start = prev.Value.AddHours(minimumTimeApartInHours);

                DateTime? @event;
                var stuck = 0;
                do
                {
                    // pick a random double, so we get minutes involved
                    var hoursToAdd = random.NextDouble()*hoursInEachSection;
                    // let's add the random hours to the start
                    // and we get our next event
                    @event = start.AddHours(hoursToAdd);

                    if (stuck++ > 5)
                        @event = end;

                // let's make sure we don't go past the window
                } while (@event > end); 

                prev = @event;
                events.Add(@event.Value);
            }

            Console.WriteLine(string.Join("\n", events));
            Console.ReadLine();
        }
    }
}