The state of Louisiana now has an online death index that presently covers the years 1911-1969. You can order copies of the death certificates by mail for a fee. The database also includes a few entries prior to 1911, but copies of some earlier records may not be available. See: Louisiana Death Records Index, 1911-1969
For more online Louisiana death indexes see: Directory of Online Louisiana Death Records Indexes and Obituaries
Thanks to Elizabeth for letting me know about the Louisiana database.