My grandmother was born in Scranton, lackawanna, PA abt. 1869, how do I get hold of a birth certificate.Born 1869 then shown in 1880 U.S. census as living with family she is recorded as niece then 1881 now shown living in Aberdare, Wales recorded as daughter, I need to establish true parentage. Any advice would be most helpful and greatly received.I have Wales 1881 census and 1911 wales census and birth certs for all children of Herbert and Hannah Rice formerly Rees
Whenever you are researching in a new time period or location, it is helpful to review what records are available for that time and place. One good starting place is the Family Search Research Wiki. According to their article Pennsylvania Vital Records, in section 1, "Vital Records Reference Dates", their coverage table says that statewide civil registration of births did not begin until 1906. Some county records are available in 1852-54, and then begin again in 1893.
There are some delayed birth records for people who were born before 1906. The FamilySearch wiki says:
Births before 1906 that were not registered at the time of the birth may have been registered beginning in 1941. To prove a birth, several witnesses were required to sign affidavits before the orphans' court which would then issue a birth certificate. Delayed registration of births began in various counties in different years, usually in 1941, and continued until about 1976.
So if no birth certificate exists, what next?
Look for other records
One thing you can do is make use of a checklist such as Sources of Genealogical Information to find other records which might have information about her birth.
Study the entire family
You don't say what else you have found out about her except for these two census records. Make a checklist of sources you have, and a timeline of her life, and write a biographical sketch. Now look for anything you can find which will fill out the picture of her entire life, because you won't know what clue will lead you to the information you want until you find it.
Does she have siblings? Sometimes there is no one record which lists her parents, but you can find the information in the records belonging to a brother or a sister. Study the entire family as a group. I was not able to find a birth record for my grandmother, but I have applications for delayed birth records for several of her siblings; I was lucky because she had three brothers and seven sisters.
What other records exist for Lackawanna County?
Searching the FamilySearch catalog for places within Pennsylvania reveals another pitfall -- under Lackawanna County, it says:
Created in August 1878 from part of Luzerne County. No counties were formed from Lackawanna Co.
So at the time of your grandmother's birth, Lackawanna County didn't exist yet. Wikipedia's article on Scranton says:
Scranton was incorporated as a borough on February 14, 1856, as a borough in Luzerne County and as a city on April 23, 1866.
When searching archives and library catalogs, search both counties.
Another thing to be aware of is that your grandmother may not have been born in Scranton itself, but in a smaller town nearby. I could not find anything about my father when I first started out, because the city I knew he was "from" was where he was living as a young man before he married. His actual birthplace was a small town in the same area. Once my brother told me the right place to look, it was easy to find his census records.
If you haven't already done so, make a list of all the sources that you have found so far, and put the events you know about in a timeline. Use the checklist of sources to fill out the picture of her later life, and work backwards from her death.
One place to start might be to look for your grandmother in the 1870 US Federal Census, and for all the other persons in the 1880 Census household you have who would have been alive in 1870.
The US National Archives has a research guide Clues in Census Records, 1850-1940, which says:
The 1870 census (column 13) and 1880 census (column 7) indicate the month in which the person was born, if born "within the year," that is between June 1, 1869 and May 31, 1870 for the 1870 census, or June 1, 1879 and May 31, 1880, for the 1880 census. The official census day was June 1 in both 1870 and 1880, although the enumerator may have visited the household at a later date.
Finally, I think it is important to remember that even if we do find a single original record which states someone's parentage, that does not constitute proof of someone's "true parentage". A single record is not proof. Original records can have mistakes -- and the parents listed on a certificate may not be the biological parents. The researcher has to follow standards -- collecting information, recording the source, analyzing it, and resolve discrepencies -- before arriving at a proof statement.