Here is some additional information on the Rankin folks you are researching. I do have photocopies of the death notices listed, if you would like them......
John A. Rankin Dead
The Girard PRESS says J. T. Rankin received a letter July 18th, informing him of the death of his son, John A. Rankin of consumption. He died somewhere in the south, where he had gone with the hope of benefiting his health. Mr. Rankin was county attorney of Crawford county two years and a prominent candidate for the same position before the republican convention last year.
The Spring Hill NEW ERA, Thursday, August 8, 1889, Vol. VI, No. 10, page 3, column 4
Died – At Longmont, Colorado, on Sunday July 14, 1889, of consumption, John A. Rankin
Mr. Rankin was an old resident of this city, and had gone to Colorado in hopes of regaining his health. He was at one time county attorney of this county, and was a highly respected and honorable citizen. A few years ago he moved to Girard, Kansas, where he was engaged in business until his health failed him. His many friends in this city will mourn his death.
The Johnson County Democrat, Thursday, July 25, 1889, Eight Year, No. 12, page 4, column 1
Longmont is in Boulder County, Colorado. I don't know which cemetery John is buried in. You will have to request some assistance there to find his grave. One thing I did find while looking around was that the Longmont Genealogy page has an index of articles that appeared in the Longmont Ledger newspaper. That listing has a reference to a DEATH article for a John A. Rankin that was published on July 19, 1889. The article may list the burial location. Maybe you can locate a microfilm of the newspaper and check for yourself. Or visit this link and request some research....
Mt. Olive Cemetery, Pittsburg, Kansas, page 138 of cemetery listing, Block 16, West Row (read South to North):
Rankin, Clara M. dau of JA & MH
Born: 11-09-1876 Died: 02-28-1891
Tombstone Transcription of All Known Cemeteries in Crawford County Kansas
William C. Cuthbertson, 108 W. Buffalo, Girard, Kansas 66743
Published in 1975
This book is approximately 11 inches high by 14 inches wide and about 1.5 inches thick. There is no master index. Each cemetery in individually indexed. The page numbers in the book start at 1 for each cemetery.
I have no idea where J.T. Rankin may be buried. You may want to start in Crawford County, KS and see if the local libraries have any obituary records. You may also want to take a look that the Deed Book records to see if he and his wife owned any property that was sold after 1910. If so, are they both listed as Grantor's? Then you may have a better idea when he died. It is possible he died while they were traveling west, and was buried where he died. In the next day or two, I will be sending an email request to a local genealogical library to have them check a marriage index they have. The Johnson County Library does not have this index. I may get lucky and find the marriage of John and Mira.