Karla, there is a town called Waupaca in a county of the same name in Wisconsin. In 1978 it was the locale of Bethany Home, Inc., 1226 Berlin St, zip 54981.
There was a special census of dependent children in 1923---to the best of my knowledge, the names of children were not collected. In this census, the institution in Waupaca was called the Danish Lutheran Bethania Orphans' Home, no address, under the auspices of United Danish Lutheran Churches. It was established in 1898.
This information is from page 413 of a book published in 1982: "Adoption Agencies, Orphanages and Maternity Homes : An Historical Directory."
The federal census of 1910 would list the inmates of all institutions as well as people living with their families or alone. Try to find an expert at census research---by reading the message boards for various counties in Wisconsin. For example, Waupaca is at :http://boards.ancestry.com/mbexec?htx=board&r=an&p=l...