I'd just like to kick it off by saying that the art involved in unbelievable.
Perform a montage with the elephants showing how species doesn't matter what sort of person you are. Live in a utopian happines with the elephants, merging into the herd and supporting their community.
Once you have their trust, lure them into smoking assorted herbs. Once they form a dependency, restrict supply and become extortionate, demanding more and more services from them for the herbs. There will doubtless be some more outspoken and troublesome of the elephants - they must be dealt with with discretion.
Even after the immediate labour needs of the tribe are fufilled, manipulate the elephants to build various megaprojects. The point of this is not to benefit from the megaprojects, but rather to change the social structure of the elephants. The once-mighty creatures, cripples by their addiction for the assorted herbs, shall live in a broken society. Living conditions for the elephants must be reduced so that they are only just surviving: they will not be aware of the long-term destruction of their society.
With time, the place of elephants will be firmly established. Broken creatures, they will beg and toil for the elves just for the next sweet hit of the assorted herbs. Elves will be established as the superior species, and as long as the living conditions of the elephants is kept poor, they will be unable to uprise and rebel. Of course, in order to maintain this, the elves need to establish a strict society: even though elves will be equal to elephants by the letter of the law, the practice will be different. By exaggerating the goblin menace as the root of all evils making scapegoats of troublesome elephants (claiming them to be agents for the goblins), a clear enemy can be established for the elephants to concern themselves with.
By offering large rewards of assorted herbs for any potential goblin agent elephants, any elephant that tries to disrupt proceedings will be quickly turned in. They will also be unable to identify with any other sympathisers, as they will not be able to tell them from the regular members of society.
A secret police will have to be established. The elephants sohuld be constantly living in fear, unable to shoe a moment's deviance from acceptable thoughts. The actual logistics of monitoring every elephant will be a huge problem, so the elephants must be unable to know if they are being watched or not. By establishing a series of underground tunnels underneath the elephant settlements where elves and elephants can be posted, the elephants will be able to be watched and heard at any time, but they will not know at any given point whether they are being monitored or not. They must therefore always act like they are being monitored, in case they are.
The knowledge and society of the elves must be heavily censored, too. The elves must establish a leader for the elephants to follow. The leader must himself be an elephant, called "prodigious pachyderm" Pictures of this leader will be placed everywhere. Since the leader is an elephant, the other elephants will be encouraged to act like him, and with time they will want to act like him. All new reaching the elephants must be completely fabriacted: they must be told how they live in an age of prosperity thanks to the glory of their leader and his following of the desired way of life, despite the filthy goblins who shall be seen as all that is bad. This leader does not need to actually exist; the elephants need to think that he exists.
Over time, a stable society will be formed. Elephants will be brainwashed into pure hatred of the goblins, and loving their leader and his agents, the elves. They shall see the leader and the elves as the source of all that is good: Their society, their defence against goblins and their assorted herbs. The mere concept of society as anything different will be outside what they can convieve: the language that they use shall have to be changed after a time to make even expressing an unfavourable thought impossible. They shall live in constant fear, though. They shall be terrified of goblin agents, and that they might be thought to be goblin agents.
Disappearances in such a society would be common, and thus nobody would notice when an elephant is taken away to be traded to the dwarves. They will not be told of the dwarves, though. Whenever an elephant is needed for trading, one shall be taken, a problematic one if preferable.