Its really quite simple, and I'm surprised whomever did the timelines for the DVD overlooked this.

(From Part II):

1. We know Vito was 9 years old when his father was killed (there's a subtitled scene telling us that).

2. We know Vito arrived in America in 1901 (he's sitting on a chair on Ellis Island when a subtitle gives us the year).

3. We know his birthday was December 7th.

OK....It definitely wasn't December when Vito arrived in America (check out the immigrants' clothing on the ship). So we can deduce that Vito was still 9 years old when he arrived (not having reached his 10th birthday yet) in 1901. That means he was born December 7, 1891.