This below is what I think could be on the original birth certificate. “Hawaii Certificate of Foreign Birth” I say think because until Obama shows his original there are multiple ways he could get a BC.
http://oeqc.doh.hawaii.gov/sites/har/AdmRules1/11-120.pdf
Certificate of birth entitled a “Hawaii Certificate of Foreign Birth” is issued. ... certificate is not evidence of United States citizenship for the child
Then he could have had it amended to late birth certificate.
http://hawaii.gov/health/vital-records/vital-records/hawnbirth.html
How to Apply for the Issuance of a Late Birth Certificate in Lieu of a Certificate of Hawaiian Birth
Upon receiving a request to amend an entry on an existing Certificate of Hawaiian Birth, the Registration Unit of the Office of Health Status Monitoring will send:
Any way we all could get certified this way...Be something if a few thousand people who have legitimate BC from other states also got one from HI....Just so we can say: “Yes we can!” ;~)
Probably not, since the Administrative Rule you link to didn't go into effect until 1981, when O would have been about twenty years old. But we do know that back in 1961, there was a provision in the Hawaii statutes allowing for a relative living in Hawaii to register the foreign birth (or out of state US birth) of a baby with the Hawaii DOH. What the title of the document such a registration would have resulted in is uncertain.