Although the 1900 census says he immigrated in 1879 it also says he was in the US for 31 years. Also his daughters Annie and Lena were born here and he appears in the 1870 census of Allegheny County. Most likely the census should have read 1869.
I suggest getting his death certificate from the PA Dept of Health. It should list his parents and possibly exactly where he was born. His obituary may or may not list his parents, but it might list exactly where he was born and any surviving siblings (at least the ones that also immigrated). Check with the Historical Society of Western Pennsylvania and the Western Pennsylvania Genealogical Society to see if they can help you with the obit.
At least one of the death certificates and marriage records for any of their children should have Catharine's maiden name.
At beta.familysearch.org they list an entry for a Peter Adler born Dec 8, 1843 to Christophori Adler and Margarethae Kraemer. Check with any LDS Family History Center about finding out more about the entry. Don't assume it is the right one. Get his death certificate and check with the Diocese Archives to confirm the connection.