The county did not get the birth information from the city of Scranton or from Carbondale, so neither would be in the county records. The films for the county births / deaths 1893-1905 are LDS. So are the films which cover births and deaths for the Scranton Board of Health, 1878-1905. You might want to try familysearch.org .
Ancestry now has access to birth and death records for the entire State of PA - the limits are 100 years for births (1905-1912) and 50 years for deaths (1905-1961); more info at the PA State Archive site (PMHC).