How long was stagecoaches active in the Indian and Oklahoma Territories?

Depends on what you mean by stage coaches and where you were in the territory. The primary purpose of "stage coaches" was to haul the mail, passengers were a bonus. In 1871, the El Paso Stage Company got the mail contract between Caddo on the Katy and Fort Sill. They used Concord coaches, then the contract passed to Patchell and Guy and they used the "mud wagon," a converted Army ambulance (the Yanks ordered thousands of the things in the Civil War and sold them as surplus afterwards; they were quite common on the frontier because of their high wheel base and construction.) After the Gulf, Santa Fe and Colorado railroad crossed the Chickasaw Nation, and railroads crossed north Texas, mail was almost exclusively hauled by the mud wagons. I can't give you an exact year because the stage gradually petered out. They were still widely operational in the 1890's, but by 1906 had been relegated to Star Route operations, hauling mail, and sometimes passengers from major mail centers to outlaying communities.

Thanks for the update on stagecoaches. That is more info than I have previously been able to uncover.

"Stagecoaches" in the sense of hauling passengers and mail were running from Caddo, Choctaw Nation to Fort Sill, I.T. during the 1870s and then in the mid-1880s the route switched from Caddo to Henrietta, Texas. I know that former Deputy U.S. Marshal Benjamin Williams who operated in the Cheyenne & Arapaho Reservation during the mid-1870s later operated a line between the Texas Panhandle and Darlington Agency.
On the Trail
Diron Ahlquist
Editor, Oklahombres Journal
OKC, OK

Regarding your question on how long stages operated, apparently they continued in operation in some areas of the state a lot longer than others. "The four members of the Davis gang, Jack and Joe Davis, Buck Burtdoff and B. Wirthman, were convicted of a stage coach robbery at Muskogee, Okla. Feb. 27, 1915. In the robbery, the bandits were wearing white sombrero hats and handkerchiefs tied over their faces. They cracked a safe and secured an express package."
Information from the Oklahoma Leader, March 4, 1915 transcribed at the Lawmen & Outlaws Site, © 2001, 2002, 2003 by Robert & Tammie Chada

Is there any information on the men who rode shotgun on the Indian Territory stagecoaches.