Eustace is tempted to be a general nuisance, proud of his own attitude. He succumbs, in the first part of the book.
Governor Gumpas has yielded to the temptation to be a petty tyrant, and to doubt that there is such a person as the real King of Narnia.
Eustace is tempted, and succumbs, to think of himself as special. One symptom is that he attempts to get water above the amount of his ration.
The rest of the crew are tempted to think "That's what he deserved," when Eustace becomes a dragon.
Eustace eventually, after being a dragon for several days, repents, and Aslan changes him back to human form. Edmund speaks comfortingly to him:
"That's all right," said Edmund. "Between ourselves, you haven't been as bad as I was on my first trip to Narnia. You were only an ass, but I was a traitor." C. S. Lewis, The Voyage of the Dawn Treader, New York: Collier Books, 1980. p. 91.
Coriakin, the magician who had been a star, did something that he shouldn't have, or failed to do something that he should have. He was punished by being put in charge of the Dufflepuds. He was tempted to impatience with them, and to not trying to educate them to maturity.
Lucy was tempted to say a spell that would have made her unnaturally beautiful. This may have been Envy. Lucy was also tempted, a short time later, to say a spell that would let her hear what others were saying about her. She yielded to this temptation, then wished that she hadn't:
"I will say the spell," said Lucy. "I don't care. I will." She said I don't care because she had a strong feeling that she mustn't.
But when she looked back at the opening words of the spell, there in the middle of the writing, where she felt quite sure there had been no picture before, she found the great face of a lion, of the Lion, Aslan himself, staring into hers. It was painted such a bright gold that it seemed to be coming towards her out of the page; and indeed she never was sure quite afterwards that it hadn't really moved a little. At any rate she knew the expression on his face quite well. He was growling and you could see most of his teeth. She became horribly afraid and turned over the page at once.
A little later she came to a spell which would let you know what your friends thought about you. Now Lucy had wanted very badly to try the other spell, the one that made you beautiful beyond the lot of mortals. So she felt that to make up for not having said it, she really would say this one. And all in a hurry, for fear her mind would change, she said the words (nothing will induce me to tell you what they were.) C. S. Lewis, The Voyage of the Dawn Treader, New York: Collier Books, 1980. pp. 130-131.
Three of the Narnian Lords were tempted to quarrel, and do so, on Ramandu's Island.
Caspian is tempted to leave the Dawn Treader, breaking his word, and neglecting his duty, in order to go on a quest that he knows is not for him. He takes steps to carry out this plan, but is dissuaded by the others, and, finally, by Aslan. He seems to be showing Pride.
You may be interested in the web site of the forthcoming Narnia movie. It has cover art for all seven Narnia books, by four different artists, the first chapter of each of the books, and a timeline of the books (which is partly speculation, of course, as Lewis didn't explicitly indicate dates).
This post is out of sequence. I thought I had posted it earlier, but obviously hadn't. Thank God for backed up files! Here is the first post in the series.