If you haven't already found it, search out Where Have the Unicorns Gone? by Jane Yolen, with gorgeous illustrations by Ruth Sanderson. It's a beautiful picture book that re-tells the myth that the unicorns have all fled to the sea and they can be spotted in the foaming waves. It's also a commentary on the industrialization of our world, if you were looking for something with a bit of a message.
Hm, I just checked on Amazon to link that picture book and it looks like Yolen has a treasury of unicorn stories, Here There Be Unicorns. It would be worth checking out. If you scroll down those pages on Amazon, there are a few other books about unicorns - Bruce Coville is another terrific author so I would check into his work too.
For chapter books, there is The Last Unicorn by Peter S. Beagle. It was NOT written for children but it is a terrific fantasy story. I haven't read it in decades but I recall there are some scenes that might be distressing to a young child - lots of tension, some chases and captivity and battles. You may want to pre-read and decide if it's appropriate.