Here is the 1850 US Census for my great great great grandmother, Sarah Dwire. I've seen the spelling as Dwyer and Dwire so I wanted to see if I could confirm the correct spelling.
I also located land grants that Sarah's father, Ellis, purchased in Illinois for Fulton, Peoria and Stark counties on November 3, 1840 which also use the Dwire spelling.
The only census I've come across that used a "y" appears to be the 1860 US Census. While there are errors on birth year as well as other spelling errors, it seems the correct spelling IS "Dwire".