Here are some articles from the Kansas papers regarding the murder of Operator Coates. According to these, two men named Harper Zerfoose and Bert Wilber were arrested and put on trial the summer of 1900, but the case was ultimately dismissed and they were released due to lack of evidence. The $600 award offered for information on the case was re-published December of 1900 and I did not find any indication that the case was ever officially resolved.
The main detective that was actively investigating the case into the next year, George C. Montgomery, was murdered himself in his own home in October of 1901 which led to many trials that went to the Kansas Supreme Court involving the '101 Ranch Cowboys'. I found more details of Detective Montgomery's murder and the 101 Ranch in the book The Real Wild West: The 101 Ranch and the Creation of the American West - Chapters 20 and 21. There is a preview you can find on Google Books.
G.C. Montgomery, Special Agent... Arkansas City Daily Traveler, Arkansas City, Kansas, Wed, Apr 11, 1900 – Page 5
He Forgot The Bike, Weekly Republican-Traveler, 05 Apr 1900, Thu, Page 8
Still Working, Weekly Republican-Traveler, 10 May 1900, Thu, Page 7
Harper Zerfoos Held, The Wichita Beacon, 17 Jul 1900, Tue, Page 5
Harper Zerfoos, Alleged Murderer of Winfield Telegrapher...The Evening Kansan-Republican, 25 Jun 1900, Mon, Page 1
For The Winfield Murder, People's Voice, 28 Jun 1900, Thu, Page 1
Caught..Supposed Murderer of Operator Coates, The Wichita Daily Eagle, 26 Jun 1900, Tue, Page 6
Bert Wilber Arrested, The Wichita Daily Eagle, 12 Jul 1900, Thu, Page 5
Zerfoose Preliminary, Arkansas City Daily Traveler, 14 Jul 1900, Sat, Page 5
Wilber Acquitted..Preliminary Hearing is Over, Weekly Republican-Traveler, 02 Aug 1900, Thu, Page 1
Harper Zerfoose Freed, Arkansas City Daily Traveler, 02 Aug 1900, Thu, Page 8
$600 Reward, The Valley Falls Vindicator, 14 Dec 1900, Fri, Page 5
The Arrest at St. Joe, Weekly Republican-Traveler, 17 Oct 1901, Thu, Page 6
Did He Kill Montgomery, The Topeka Daily Capital, 05 Feb 1902, Wed, Page 1