Apply after January 1st because AMEX dates new cards with the current month and the original membership year. So if your original year was 2009, and you applied today, the new card would have an opening date of 12/2009 (one year old). If you wait a couple days and apply on January 1st, your opening date for the new card will be 1/2009 (two years old). So if I were you I would apply for a new card, but I would wait a couple of days to gain an additional year of age on the new card.

Good luck!