Quay is an unincorporated community and census-designated place located on the boundary line between Pawnee and Payne counties in the U.S. state of Oklahoma. The population was 47 at the 2000 census, when it was still a town; the community disincorporated on August 23, 2000. No population was recorded in the census of 2010. But the 2020 Censu…Quay is an unincorporated community and census-designated place located on the boundary line between Pawnee and Payne counties in the U.S. state of Oklahoma. The population was 47 at the 2000 census, when it was still a town; the community disincorporated on August 23, 2000. No population was recorded in the census of 2010. But the 2020 Census recorded 39 persons.