In Ruby, is there a way to 'override' a constant in a subclass so that inherited methods use the new constant instead of the old?

I've done this by simply redefining the constant in the subclass, and then referring to it in methods as self.class::CONST in instance methods and self::CONST in class methods. In your example:

class SuperClass
  CONST = "Hello, world!"
  def self.say_hello
    self::CONST
  end
end

class SubClass < SuperClass
  CONST = "Hello, Bob!"
end

SubClass.say_hello #=> "Hello, Bob!"

You can refer to a constant like this in the parent class:

For a instance method: self.class::CONST

For a self method: self::CONST

class SuperClass
  CONST = "Hello, world!"
  def print_const
    puts self.class::CONST
  end

  def self.print_const
    puts self::CONST
  end

end

class SubClass < SuperClass
  CONST = "Hello, Bob!"
end

SubClass.new.print_const #=> "Hello, Bob!"
SubClass.print_const #=> "Hello, Bob!"

If you have the luxury of being able to change the base class, consider wrapping the "constants" that need changing in class methods in the base class and overriding them as needed in subclasses. This removes the potential for confusion between parent and subclass constants. For the example, this would be as follows:

class SuperClass
  CONST = "Hello, world!".freeze

  def self.const
    CONST
  end

  def self.say_hello
    const
  end
end

class SubClass < SuperClass
  CONST = "Hello, Bob!".freeze

  def self.const
    CONST
  end
end

SubClass.say_hello #=> "Hello, Bob!