According to the Magazine Data File, Ainslee's Magazine began as The Yellow Kid (the comic), but switched to Ainslee's in 1898 (as a general magazine) then to all-fiction in 1902. Its authors include Bret Harte, Anthony Hope, Stephen Crane, Jack London, O. Henry, Albert Payson Terhune, E. Phillips Oppenheim, among others.
(logista) has several random issues. They are popular with collectors because of their covers (sometimes for their content) and difficult to find inexpensively.
|12; Sep 1903||logista|
|15; Jun 1905||logista||Ainslee's Magazine [15:5] (1905): Completed and Posted to Project Gutenberg|
|15; Jul 1905||logista||Ainslee's Magazine [15:6] (1905): Completed and Posted to Project Gutenberg|
|16; Sep 1905||logista||Ainslee's Magazine [16:2] (1905): Completed and Posted to Project Gutenberg|
|16; Oct 1905||logista||Ainslee's Magazine [16:3] (1905): Completed and Posted to Project Gutenberg|
|16; Nov 1905||logista|
|16; Jan 1906||logista|
|17; Feb 1906||logista|
|17; Mar 1906||logista|
|17; Apr 1906||logista|
|17; May 1906||logista|
|17; Jun 1906||logista|
|18; Dec 1906||logista|
Hathi Trust has some volumes as of May 2013: 3-10:no1-6, 12-13.