"Coherent" is perfectly fine in the two examples from the dictionary that you cite. I would not use it when talking about a person being consistent with himself.
But if you are refering to this sentence:
His work is an instant revelation, a reflection of the most personal concerns that he always felt with intensity, never crushed by swindles with money and always coherent with his convictions.
Then saying coherent with his convictions also means coherent with himself since his convictions are also "himself" right?
Also I found examples used in articles like:
In so doing he has been above all
coherent with himself and his vision of the United States and its history and culture.
Or:
And yet the deficiency of the accord between the Koranic references and the Bible stories themselves show that Mohammed was
not consistent (coherent) with himself.
In this case is also clear that the author considered the words consistent and coherent quite similar if not the same.
Or:
Kane is a like a real person, always
coherent with himself, but never banal or predictable:
Or:
And, when we reach that farther shore, we discover a man who is sensitive and honest,
coherent with himself and with the world around him.
So, now I am quite confused.