How do I create a constant that is an array?

Strictly speaking you can't, since const can only be applied to a field or local whose value is known at compile time.

In both the lines below, the right-hand is not a constant expression (not in C#).

const int [] constIntArray = newint [] {2, 3, 4};
 // error CS0133: The expression being assigned to 'constIntArray' must be constant
const int [] constIntArrayAnother = {2, 3, 4};
 // error CS0623: Array initializers can only be used in a variable or field
 //               initializer. Try using a new expression instead.

However, there are some workarounds, depending on what it is you want to achieve.

If want a proper .NET array (System.Array) that cannot be reassigned, then static readonly will do for you.

static readonly int [] constIntArray = new int[] {1, 2, 3};

The constIntArray field will be initialized before it its first use.

If, on the other hand, you really need a const set of values (say as an argument to an attribute constructor), then - if you can limit yourself to integral types - an enum would serve you well.

For example:

[Flags]
public enum Role
{
 Administrator = 1,
 BackupOperator = 2,
 // etc.
}

public class RoleAttribute : Attribute
{
 public RoleAttribute()
 {
  CreateRole = DefaultRole;
 }

 public RoleAttribute(Role role)
 {
  CreateRole = role;
 }

 public Role CreateRole
 {
  get { return this.createRole; }
  set { this.createRole = value; }
 }

 private Role createRole = 0;
 public const Role DefaultRole = Role.Administrator
   Role.BackupOperator;
}

[RoleAttribute(RoleAttribute.DefaultRole)]
public class DatabaseAccount
{
 //..............
}

RoleAttribute, instead of taking an array, would only take a single argument of flags (appropriately or-ed). If the underlying type of the Role enum is long or ulong, that gives you 64 different Roles.