Spanish Cedar is far and above the best choice and mahogony is about the only acceptable alternative. Quite frankly ChasDen will build you some beautiful drawers for not much more than you can buy the Spanish Cedar for in small quantities - takes a while to get them though as he stays very busy but worth the wait.
If you are not able to use Spanish Cedar my best suggestion would be not to use drawers but just stack some good unfinished spanish cedar cigar boxes in there. You can get boxes at most B&M's and find some you like just ask them to hold on to those for you as they become available.
