'special relationship' is a subjective term, but I am aware of what you mean and my answer would be no there is not. While they may be allies, my justification is that since 9/11, the U.S. has tended to move away from 'insider' or 'special' relations with other countries. Now more than ever, global politics is an every-state-for-himself game.
A good example is border security. Canada used to be considered in a 'special relationship' with the U.S., but more and more the Americans are saying, "Sorry Canada, but if we treat our Mexican border a certain way, then that becomes our policy and you will be treated in a similar manner." It might make no sense, since we tend to move more products than people, and it might even hurt trade relations....but this is the reality of Congress.