Here is an antedating slightly older than the one posted above by JEL. It too is from Springfield Globe-Republic (8 August 1886, p. 1):
“Next week, get a tent, put ‘t over his nibs, charge two jitneys to git in. Money? Well, ax me. Pard, we ain’t much on looks, but we’re some on gettin’ there.”
It may be possible to antedate the word (which has been spelled jetney, gitney, and jitney) to the 1870s:
"Does jitney mean a nickel, or a ride, or a method of transportation, or a state of mind? Apparently it now means transportation, whether it means transportation for a nickel or not is disputed. Certainly the term 'jitney,' before the jitney boom arose, meant a small coin, a cent, five cents, a dime, or a quarter. As a boy in San Francisco, the writer has heard and used the term 'jitney,' meaning either a nickel or a dime. Cents in those days were unheard of on the coast. Later, in New Orleans, the term jitney was often heard, but there it seemed to refer to a nickel alone. May we advance a theory? The jitney, we think, originated in Louisiana in the Creole word, 'jetton,' meaning a counter, or poker chip. It did not necessarily mean a nickel, because this was in the days before nickels were invented, and in Louisiana until the time of the civil war circulated a miscellaneous assortment of Spanish, French and South American coin. Therefore, jitney meant the smaller denominations of these coin—sous and pesos and what not. From Louisiana the term naturally traveled to California. It has been in use there since the days of '49. How do I know? Three reasons: first, we infer that the word was in common use because we had learned it there; secondly, because several pioneers have told us it was used; thirdly, because in reading the old files of the Overland Magazine some time ago, dated in the seventies, ]I found that the term jitney is used by one of the characters of a story of San Francisco life, the context of the story shows that this particular 'jitney' was a quarter. A further proof that a jitney is not necessarily a nickel is that in early times no coin of less value than a quarter circulated on the coast.
"So. Mr. Jitneur, when some opponent upbraids you for not being a true jitney because you may charge more than five cents, read him this article and crush him to earth. A jitney is a small coin, such as the great American public are now paying for trackless transportation.
"Postscript—Alas, for trying to prove anything! We have just received word that a Canadian board of councilmen have decided that a 'jitney' is five cents" (unsigned, "What does Jitney Mean?," The Jitney Bus, vol. 1, no. 4, July 1915, p. 114; the bracketed addition is mine).
I say "may be possible to antedate," because the passage of time (cf. "some time ago") may play tricks on one's memory. Issues of The Overland Monthly have to examined line by line.
The anonymous writer's speculation in the rest of the passage is likewise subject to examination. Nothing is to be taken on faith, such as his inference that "the word was in common use because we had learned it there" and his reasoning that the word had been used in California "since the days of '49 [...] because several pioneers have told us it was used."
Also, since five-cent coins have been minted in the United States since the 1790s, the writer's ability to know what the situation was "in the days before nickels were invented" is doubtful.
A supplement to the following chapter is now in preparation:
Gold, David L. 2009. “American English jitney 'five-cent coin; sum of five cents' Has No Apparent Jewish or Russian Connection and May Come from (Black?) Louisiana French jetnée (On the Increasing Difficulty of Harvesting All the Grain).” In his Studies in Etymology and Etiology (With Emphasis on Germanic, Jewish, Romance, and Slavic Languages). Selected and edited, with a foreword, by Félix Rodríguez González and Antonio Lillo Buades. Alicante. Publicaciones de la Universidad de Alicante. Pp.163-192 [partly available here: https://books.google.com/books?id=l015C5vm1XkC&q=jitney#v=snippet&q=jitney&f=false].
The supplement will, inter alia, examine the suggestion that the word jetney ~ gitney ~ jitney comes from jeton ~ jetton and the suggestion that it comes from jetnée. The evidence is strong that both suggestions are indefensible. The supplement will propose a different immediate etymon for the English word.