There are a bunch of resources that encourage kids to read over the summer. Libraries and book stores offer summer reading programs with prizes. Having a group of friends to share your favorite books with, though, can make reading that much more fun.
If you want to start a children's book club for the summer, I suggest keeping it fun. Pick books that the kids would probably not read in school, and don't worry if they have a lot of 'literary value'. If your child is interested, you could pick a theme, like books about dragons, or superheros, or books with strong girl leads. Think about what the kids you want to invite like. Maybe you pick books that have a film adaptation you could watch after you finish the book. Let the kids talk about what they want, and just be ready to throw out a question or idea if they run out of things to discuss on their own.
Maybe have a snack or craft to go along with the book if it lends itself to such things.