There is a group of books in the Dubrovnik Archive that contains transcriptions of all Christening and marriage records for the town of Korc"ula [Korcula], from the late 1500s into the 1900s, as follows:
Christening: 1583-1946 (11 books)
Marriage: 1585-1905 (3 books)
They have not been indexed. Here is a photo of a cover.
These were compiled from around 1979 to the late 1980s by Ante Kalogjera who was born in Blato, Korc"ula, in 1910 and was a professor in Split. The first 2 books are in his own handwriting but then he switched to a typewriter. Here are samples:
Handwritten, from a Christening book, 1644 (29 July). Typewritten, from a Christening book, 1780. Birth (r) is also given in the bottom example, but most entries have Christening dates only.
The books are bound but are printed on only one side of the paper, and may very well be simply bound photocopies. It is doubtful that more than 3 or 4 copies of these books exist. Such a wide, unbroken span of records is a rarity in Croatia (I know of no other), and in fact can seldom be found anywhere in the world. If your family is from the town of Korc"ula (on the island of Korc"ula), you are very lucky.
Below is a sampling (probably less than 30%) of the surnames from one of these books (Christening book, around 1830). The names in parentheses are there for people who may be searching under variant spellings.
Records from these books can be checked or photographed for your purposes. Contact Tom Ninkovich, here.