Hi
Having looked Googled Wikipedia on extinct birds it does mention the Jamaician Petrel:
Possibly a subspecies of the Black-capped Petrel; unconfirmed reports suggest it might survive. Officially classified as critically endangered, possibly extinct.
This species was last collected in 1879, and was searched for without success between 1996 and 2000. However, it cannot yet be classified as extinct because nocturnal petrels are notoriously difficult to record, and it may conceivably occur on Dominica and Guadeloupe.
Don't know whether this helps.