Examples of monologue books for young actors, all easily found online or ordered from your local bookstore:

Echo Booming Monologues: 100 Monologues for Teens (Paperback)
    by Mary Depner
    

The Ultimate Audition Book: 222 Comedy Monologues, 2 Minutes And Under Vol. 4 (Monologue Audition Series) by Irene Ziegler Aston
   
The Ultimate Audition Book: 222 Monologues 2 Minutes and Under (Monologue Audition Series) by Jocelyn A. Beard
   
The Actor's Book of Contemporary Stage Monologues: More Than 150 Monologues from More Than 70 Playwrights by Nina Shengold

The Ultimate Audition Book for Teens: 111 One-Minute Monologues (Young Actors Series) by Janet B. Milstein

The Ultimate Audition Book for Teens 2: 111 One-Minute Monologues (Young Actors Series) by L. E. McCullough

My First Monologue Book: 100 Monologues for Young Children (Young Actors) (Paperback)
by Kristen Dabrowski (Author)

Cool Characters for Kids! 71 One-Minute Monologues, Ages 4-12 (Paperback)
by Janet B. Milstein (Author)