Just spent an enjoyable hour testing and killing elephants and I have to say without a doubt the best and safest way to kill them quickly and efficiently is with javelinmen, mounted or no, although if they are infantry javelinmen then one on one may not be your friend, but it's not a major issue to recruit one more unit!
Aced up Longbowmen behind stakes suffered 70-80 casualties to no kills by the time the elephants reached them, with or without using flaming ammunition, and Janissary musketeers wounded a couple but killed none before they had the reforming problem, which is the only bug I've really noticed and had a problem with and at the minute is a reason to not recruit any musketeers ever.
However the javelinmen on average had 1-2 elephants killed in the first volley, and about 4 more volleys to finish them off or have them running amok.
Since RTW I have no desire to engage elephants in close combat, it isn't really a viable option and the kills/losses ratio is generally pretty poor.
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