“Dallasite” is the name of an inhabitant of Dallas, Texas. The name “Dallasite” has been cited in print since at least 1873.
 
The name “Dallasonian” for an inhabitant of Dallas has been very rarely cited in print.
 
 
Wikipedia: Demonym
Dallas → Dallasite
 
Wikipedia: Dallas
Dallas ( /ˈdæləs/) is the third-largest city in Texas and the ninth-largest in the United States. The Dallas-Fort Worth Metroplex is the largest metropolitan area in the South and fourth-largest metropolitan area in the United States. Divided between Collin, Dallas, Denton, Kaufman, and Rockwall counties, the city had a population of approximately 1.2 million, in 2010 according to the United States Census Bureau.
 
The city is the largest economic center of the 12-county Dallas–Fort Worth–Arlington metropolitan area (the DFW MSA) that according to the March 2010 U.S. Census Bureau release, had a population of roughly 6.5 million as of July 2009. The metroplex economy is the sixth largest in the United States, with a 2010 gross metropolitan product of $374 billion.
 
Dallas was founded in 1841 and was formally incorporated as a city in February 1856. The city’s economy is primarily based on banking, commerce, telecommunications, computer technology, energy, healthcare and medical research, transportation and logistics. The city is home to the third largest concentration of Fortune 500 companies in the nation. Located in North Texas and a major city in the American South, Dallas is the main core of the largest inland metropolitan area in the United States that lacks any navigable link to the sea.
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Demonym Dallasite
 
Free Merriam-Webster Dictionary
Dal·las geographical name \ˈda-ləs, -lis\
Definition of DALLAS
city NE Texas on Trinity River pop 1,188,580
— Dal·las·ite \ˈda-lə-ˌsīt\ noun
 
19 November 1873, Galveston (TX) Tri-Weekly News, pg. 1, col. 9:
Alleged Robbery.—A Dallasite was before his honor, the Recorder, Satuday, charged with swindling an old man out of $40 by cards. The Dallasite looked rather shaky about it, and is said to have “roped in” his victim.
 
The Portal to Texas History
15 March 1875, Intelligencer-Echo (Austin, TX), pg. 1, col. 3:
Dallasites take wood at $4 and $5 a cord and eggs at 20 and 25 cents a dozen.
 
19 February 1876, Pomeroy’s Democrat (Chicago, IL), pg. 3, col. 3:
Well, Dallas will do; the centre of the world; every evidence, the Dallasites claim, or the sky is higher overhead than any place else, then it approaches the earth all around!
 
OCLC WorldCat record
The Dallasite
Publisher: Dallas, Tex : R.C. Dyer & Co., 1929-
Series: (MN *ZZAN-25014). 
Edition/Format:  Journal, magazine : Periodical : Microfilm : Master microform : English
       
OCLC WorldCat record
Some of my best friends are green : Dallasites share their horticultural secrets
Author: Marianne Scruggs Junior Garden Club.
Publisher: Dallas, Tex. : Marianne Scruggs Junior Garden Club, 1972.
Edition/Format:  Book : English

OCLC WorldCat record
Curse of the murdered witch
Author: Marcel D’Edwin
Publisher: Mesquite, Tex. : Dallasite Publications, 1984.
Edition/Format:  Book : Fiction : English
 
OCLC WorldCat record
Looking back : a Dallasite’s recollections from the Roaring Twenties to the new millennium
Author: William E Mott
Publisher: [Dallas, Tex.? : W.E. Mott?], ©2006.
Edition/Format:  Book : English
 
D Magazine (Dallas, TX)
Are We Dallasites or Dallasonians? Fort Worthers or Fort Worthians? Etymology Tells Us Who We Are
Posted on January 5th, 2012 4:26pm by Jason Heid
Barry Popik, a lawyer in Austin, likes words. He spends a lot of time researching the history of familiar phrases. He once went to great lengths to convince Nancy that hamburgers weren’t invented in Texas. He has a website on which he discusses the etymology of a host of terms, posts photos of himself with New York Mayor Michael Bloomberg, and otherwise makes it clear that his intellect is superior to yours.
 
Part of his site is devoted to assembling a “Lone Star Dictionary,” and lately he’s been adding to it with a series of posts about the history of terms for referring to the inhabitants of specific geographic locations. I’m sorry to say that “Dallasite” appears to be the only legitimate option for those of here in the region’s biggest city.