Is it possible to set private property via reflection?

Yes, it is:

/// <summary>
/// Returns a _private_ Property Value from a given Object. Uses Reflection.
/// Throws a ArgumentOutOfRangeException if the Property is not found.
/// </summary>
/// <typeparam name="T">Type of the Property</typeparam>
/// <param name="obj">Object from where the Property Value is returned</param>
/// <param name="propName">Propertyname as string.</param>
/// <returns>PropertyValue</returns>
public static T GetPrivatePropertyValue<T>(this object obj, string propName)
{
    if (obj == null) throw new ArgumentNullException("obj");
    PropertyInfo pi = obj.GetType().GetProperty(propName, BindingFlags.Public | BindingFlags.NonPublic | BindingFlags.Instance);
    if (pi == null) throw new ArgumentOutOfRangeException("propName", string.Format("Property {0} was not found in Type {1}", propName, obj.GetType().FullName));
    return (T)pi.GetValue(obj, null);
}

/// <summary>
/// Returns a private Property Value from a given Object. Uses Reflection.
/// Throws a ArgumentOutOfRangeException if the Property is not found.
/// </summary>
/// <typeparam name="T">Type of the Property</typeparam>
/// <param name="obj">Object from where the Property Value is returned</param>
/// <param name="propName">Propertyname as string.</param>
/// <returns>PropertyValue</returns>
public static T GetPrivateFieldValue<T>(this object obj, string propName)
{
    if (obj == null) throw new ArgumentNullException("obj");
    Type t = obj.GetType();
    FieldInfo fi = null;
    while (fi == null && t != null)
    {
        fi = t.GetField(propName, BindingFlags.Public | BindingFlags.NonPublic | BindingFlags.Instance);
        t = t.BaseType;
    }
    if (fi == null) throw new ArgumentOutOfRangeException("propName", string.Format("Field {0} was not found in Type {1}", propName, obj.GetType().FullName));
    return (T)fi.GetValue(obj);
}

/// <summary>
/// Sets a _private_ Property Value from a given Object. Uses Reflection.
/// Throws a ArgumentOutOfRangeException if the Property is not found.
/// </summary>
/// <typeparam name="T">Type of the Property</typeparam>
/// <param name="obj">Object from where the Property Value is set</param>
/// <param name="propName">Propertyname as string.</param>
/// <param name="val">Value to set.</param>
/// <returns>PropertyValue</returns>
public static void SetPrivatePropertyValue<T>(this object obj, string propName, T val)
{
    Type t = obj.GetType();
    if (t.GetProperty(propName, BindingFlags.Public | BindingFlags.NonPublic | BindingFlags.Instance) == null)
        throw new ArgumentOutOfRangeException("propName", string.Format("Property {0} was not found in Type {1}", propName, obj.GetType().FullName));
    t.InvokeMember(propName, BindingFlags.Public | BindingFlags.NonPublic | BindingFlags.SetProperty | BindingFlags.Instance, null, obj, new object[] { val });
}

/// <summary>
/// Set a private Property Value on a given Object. Uses Reflection.
/// </summary>
/// <typeparam name="T">Type of the Property</typeparam>
/// <param name="obj">Object from where the Property Value is returned</param>
/// <param name="propName">Propertyname as string.</param>
/// <param name="val">the value to set</param>
/// <exception cref="ArgumentOutOfRangeException">if the Property is not found</exception>
public static void SetPrivateFieldValue<T>(this object obj, string propName, T val)
{
    if (obj == null) throw new ArgumentNullException("obj");
    Type t = obj.GetType();
    FieldInfo fi = null;
    while (fi == null && t != null)
    {
        fi = t.GetField(propName, BindingFlags.Public | BindingFlags.NonPublic | BindingFlags.Instance);
        t = t.BaseType;
    }
    if (fi == null) throw new ArgumentOutOfRangeException("propName", string.Format("Field {0} was not found in Type {1}", propName, obj.GetType().FullName));
    fi.SetValue(obj, val);
}

t.GetProperty("CreatedOn")
    .SetValue(obj, new DateTime(2009, 10, 14), null);

EDIT: Since the property itself is public, you apparently don't need to use BindingFlags.NonPublic to find it. Calling SetValue despite the the setter having less accessibility still does what you expect.

You can access private setter from derived type via code

public static void SetProperty(object instance, string propertyName, object newValue)
{
    Type type = instance.GetType();

    PropertyInfo prop = type.BaseType.GetProperty(propertyName);

    prop.SetValue(instance, newValue, null);
}

None of these worked for me, and my property name was unique, so I just used this:

public static void SetPrivatePropertyValue<T>(T obj, string propertyName, object newValue)
{
    // add a check here that the object obj and propertyName string are not null
    foreach (FieldInfo fi in obj.GetType().GetFields(BindingFlags.Instance | BindingFlags.NonPublic))
    {
        if (fi.Name.ToLower().Contains(propertyName.ToLower()))
        {
            fi.SetValue(obj, newValue);
            break;
        }
    }
}