The kind of cat that vito is holding in the Godfather part 1 is a Havana brown cat(which ironically isn't always brown like in the movie.) These cats weren't developed until the 1950s. The opening scene takes place before the cat was even in existance

I got this from the website
The Havana Brown cat was developed in the 1950s by crossing a British Seal Point Siamese with another black shorthaired cat of Siamese descent. These cats were formerly known as Chestnut Brown Foreigns. Once American breeders started developing and raising these cats the British and United States varieties began to take on different but similar characteristics.