“Dallasonian” is the name of an inhabitant of Dallas, Texas. The name “Dallasonian” has been cited in print since at least 1932, but has been very rarely used.
 
An inhabitant of Dallas is usually called a “Dallasite.”
 
 
Wikipedia: Dallas
Dallas ( /ˈdæləs/) is the third-largest city in the state of 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 1,197,816 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 6,371,773 as of the 2010 U.S. Census. 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.
 
The city’s prominence arose from its historical importance as a center for the oil and cotton industries, and its position along numerous railroad lines. With the advent of the interstate highway system in the 1950’s and 1960’s, Dallas became an east/west and north/south focal point of the interstate system with the convergence of four major interstate highways in the city, along with a fifth interstate loop around the city. Dallas developed a strong industrial and financial sector, and a major inland port, due largely to the presence of Dallas/Fort Worth International Airport, one of the largest and busiest airports in the world.
       
22 August 1932, Dallas (TX) Morning News, “‘Shinganhi’ Heard at Bowl” by John Rosenfield Jr., sec. 1, pg. 5, col. 4:
A record crowd went to the Bowl Sunday night to hear music that was both American and Dallasonian.
 
3 March 1946, San Antonio (TX) Express, “Dallas racks up twin win in area volleyball,” pg. 2C, col. 2:
The Dallasonians turned back Houston, 15-17, 15-8, in the vet class, and also defeated the Houston open team, 15-1, 18-16.
 
15 July 1968, Seattle (WA) Daily Times, “If It Sounds Good, It’s Best…Ah?” by Byron Fish, pg. 9, col. 2:
“Dallas, Dallans…”
“No, no, the people of Dallas are Dallasers…er, Dallasites…Dallasonians…forget ‘em! It’s only one town in Taxen…we mean, Texas, anyway.”
 
Google Books
The Highbinders
By Oliver Bleeck
New York, NY: Morrow
1974 [©1973] 
Pg. 92:
A good Saturday night player, riding his luck, would have raised me a hundred pounds and that’s what the Dallasonian did. I suppose you call the citizens of Dallas Dallasonians. Or Dallasites. I’ve never really thought about it.
     
NPR
The Dallas Wind Symphony 
May 16, 1997
The Dallas Wind Symphony plays the Variations on “America” by Charles Ives. Under the direction of Jerry Junkin, the Dallasonians performed the work as part of a February 27 concert at Meyerson Symphony Center in Dallas, Texas.
 
Google Books
An Angel for Maxey
By Ronald C. Winters
[S.l.] : West Bow Press
2010
Pg. 99:
On the phone with Jan he told her he was beginning to feel like a “Dallasite.” She said a “Dallasonian”; they both laughed not knowing which noun was the correct one.
 
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.