The original Peter Pan, or, The Boy Who Never Grew Up.
If we’re looking for a book that’s completely without violence, conflict, or anything threatening or unpleasant, Winnie the Pooh would seem like an obvious choice.
Take a look at the 2 other E.B. White books instead of Charlotte’s Web. His Stuart Little is a lot of fun (if you think that she won’t be upset at the idea of a human mom giving birth to a mouse) and so is The Trumpet of the Swan.
Would the Chicken Soup for the Soul books be of interest? They contain some conflict but it’s always resolved in a positive way.
Anything by Beverly Cleary, perhaps?
How about the Mrs. Pollifax series by Dorothy Gilman? They are charming.
If she likes to be read to and go on drives I would suggest an audiobook or two wouldn’t be a bad move. Many of the titles mentioned are available. For great reading Stephen Fry has done the Winnie The Pooh books, the Paddington books and some Roald Dahl. There is a great collection of Dr Seuss read by people like John Lithgow, Dustin Hoffman and Kelsey Grammer that makes for good quote-along amusement in the car.
Poetry might be a good idea. I know someone with autism who loves haiku.
There are several picture book versions of episodes in his memoirs, which might be a good idea, too, or instead.
Not really–there’s the swarm of bees, Pooh stuck in Rabbit’s doorway, possible rampaging heffalumps, the blustery day, the kidnapping of Roo, the flood and probably more if we look at the book.
I don’t know if these are still commercially available, but the Danny Dunn and Henry Reed, Inc. series might be in this lady’s comfort zone. So might Misty of Chincoteague.
The humorous short story collections by Patrick McManus. Most of the “scary” bits are led up to in ways that make them funny, because you know what the “scaree” doesn’t. And McManus has a gift for descriptions of absurd situations that adds to the humor.
Oh god, is he the one with the description of riding a bike downhill with a “dead” deer? I laughed like an idiot at that one.
You may have conflated two stories, but yes. 
He tells of hunting on a bicycle and not realizing he had only knocked out the deer until it woke up as he was carrying it home piggyback on the bike.
The downhill one was his older cousin and a friend commandeering his bike to avoid walking back to town down a long straight hill, and not giving him the chance to tell them there were no brakes.
Ah! Well, conflation or no, he’s really funny. 