Michael Schwartz Library
Population of States and Counties in the United States: 1790-1990 -- Ohio is on pages 124 to 129, in two batches: 1890-1990 and 1800-1880.
The Real Property Inventory (1932-1980s) volumes on Cleveland demographics are contained in Special Collections and other libraries. Howard Whipple Green's article on the RPI.
Indexes to the RPI's Sheet-A-Week newsletters, Vol.1-10: Part 1 and Part 2
Current census data, for comparison:
Useful links for local data: