Is it possible to negate a scope in Rails 3?

In Rails 4.2, you can do:

scope :original, -> { ... original scope definition ... }
scope :not_original, -> { where.not(id: original) }

It'll use a subquery.

I wouldn't use a single scope for this, but two:

scope :with_missing_coins, joins(:coins).where("coins.is_missing = ?", true)
scope :without_missing_coins, joins(:coins).where("coins.is_missing = ?", false)

That way, when these scopes are used then it's explicit what's happening. With what numbers1311407 suggests, it is not immediately clear what the false argument to with_missing_coins is doing.

We should try to write code as clear as possible and if that means being less of a zealot about DRY once in while then so be it.

There's no "reversal" of a scope per se, although I don't think resorting to a lambda method is a problem.

scope :missing_coins, lambda {|status| 
  joins(:coins).where("coins.is_missing = ?", status) 
}

# you could still implement your other scopes, but using the first
scope :with_missing_coins,    lambda { missing_coins(true) }
scope :without_missing_coins, lambda { missing_coins(false) }

then:

Collection.with_missing_coins
Collection.without_missing_coins