This title was published in a number of different countries. Here is the information about the Australian version.

E. W. Cole, Book Arcade, Melbourne, Australia
This Australian company published A Bad Boy’s Diary by Little Georgie in approximately 1920. It is in wraps at 7 x 5.

Edward William Cole (1832-1918). He began as a Melbourne bookseller in 1865. Cole founded the Book Arcade in 1883. In addition to the Arcade, Cole had a book publishing line of which this book is an example.

For more about Cole – see http://adb.anu.edu.au/biography/cole-edward-william-3243

This book was written by Metta Victoria Fuller Victor 1831-1885 (pseudonym- Walter T. Gray). The Little Georgie pseudonym was used for this edition.

I have seen two different editions of this title which were published by Cole. The Bad Boy and the Professor are in red in the earlier one. The title page of this format lists only one address for Cole. In the other (presumed later) book there are several Cole addresses. Cole first published this title in 1920

Both books are in wraps, 7.25 x 5, and have the same text in 135 pages.

I do not know if there are any other Cole formats.