Another find from Newspaperarchives.com... some time ago Jesse
Sheidlower gave the earliest known cite for "(have got) another thing
coming", from 1959:

     http://groups.google.com/groups?selm=cactff$sm...@panix2.panix.com

     1959 Lethbridge (Alberta, Canada) Herald 22 Aug. 20/3 Please
     tell your friends in France that if any more come over here
     thinking they can put money in slot machines and get money
     galore, they have got another thing coming.

That newspaper is part of the Newspaperarchives.com collection, so I
assume that's where the cite was found.  But the archive continues to
grow, and it now includes a cite antedating that one by forty years:

     Syracuse (NY) Herald, August 12, 1919
     PITY THE POOR MOVIE STAR
     If you think the life of a movie star is all sunshine and
     flowers you've got another thing coming.

There are a few other cites from the '20s, so it's not an isolated case.
The earliest cites I've found for "another think coming" are from 1900:

     Daily Iowa State Press, July 7, 1900
     An Iowa county man writes to a Des Moines paper that he
     thinks Capt. J.N.W. Rumple, of Marengo, will be nominated
     by acclamation for Joe R. Lane's place in congress.  We
     think the Iowa county man has another think coming.

     Anaconda (Montana) Standard, November 7, 1900  
     "I wouldn't trust you judges anyhow.  I think you
     flim-flammed him."
     "Well, you've got another think coming if you can stand
     the shock.  We ain't like those guys in your party.  
     We're on the square."