Can a notary notarize a copy of a birth certificate? 

Notaries are advised to stay away from notarizing copies of vital records including birth certificates, marriage certificates, and death certificates.  The state and/or county clerks are in charge of vital records.  Just politely decline when asked to notarize a signature on a birth certificate.  These types of vital records must be certified by the county clerk in the corresponding county.
 
No place to sign!
Additionally, there is no place for a signer to sign on a birth certificate, so how can you notarize a document without a signature?  Conceivably, you could draw up an Affidavit that claims that the copy is a true and complete copy of the original birth certificate.  The signer could sign that affidavit, and you could notarize the signature on the affidavit and give them a quick oath. But, this is not legal in many states in conjunction with a birth certificate.

 What should a notary do?
As a notary, you should know the name of the document that is to be notarized BEFORE you get in your car.  Imagine driving 45 minutes in traffic only to find out that you are going to be asked to notarize a birth certificate. Have fun getting your travel fee in that case when you tell the client, “no can do”. 
 
Fetal Death Certificates?
I never knew this existed until I read someone’s reply to a forum post about notarizing (or not notarizing) birth certificates.  I never knew there was such thing as a fetal death certificate.  How can you give a certificate to someone who has not yet been named?  Do souls have an SKU number?  Was the fetus mature enough to have been infused with a soul yet?  When you study spirituality, you start asking questions like this!  On a brighter note, the fetus will be reincarnated, and won’t suffer much according to a colleague who specializes in past life regression!
 
Refer them to an Attorney
When asked to do questionable or illegal acts, just refer your client to an Attorney so that they can get a professional answer.
 
 
You might also like:
 
Can I notarize a birth certificate – forum discussion http://www.123notary.com/forum/topic.asp?TOPIC_ID=3924

How to get something notarized that doesn’t have a signature
http://blog.123notary.com/?p=4695

The chicken & egg: Birth Certificate problem solved
http://blog.123notary.com/?p=3474