Since the API relies on something that is not available, its service is unavailable as well.
I would think that the status code 503: Service Unavailable is the best fit for your situation. From the RFC description:
The server is currently unable to handle the request due to a temporary overloading or maintenance of the server. The implication is that this is a temporary condition which will be alleviated after some delay. If known, the length of the delay MAY be indicated in a Retry-After header. If no Retry-After is given, the client SHOULD handle the response as it would for a 500 response.
Granted, the description implies that this status code should be applied for errors on the server itself (and not to signal a problem with an external dependency). However, this is the best fit within the RFC status codes, and I wouldn't suggest using any custom status codes so anyone can understand them.
Alternatively, if your API supports a way of communicating errors (e.g. to tell the user that the ID he supplied is incorrect) you may be able to use this method to tell the user that the dependency is unavailable. This might be a little friendlier and might avoid some bug searching on the user's side, since at least some of the users won't be familiar with any status codes besides 403, 404 and maybe 500, depending on your audience.