I found a website that lists the Top 40 Mardi Gras Songs

Those songs are:

1) Big Chief Part - Professor Longhair   
2) Knock With Me - Rock With Me - Little Rascals Brass Band
3) Carnival Time - Al Johnson
4) Go To The Mardi Gras - Professor Longhair
5) Street Parade - Earl King
6) I Luv me sum Mardi Gras - Tha Nu Jaz Orda      
7) Mardi Gras Mambo - Meters
8) New Suit - The Wild Magnolias
9) Second Line - Stop, Inc.
10) Congo Square - Cyril Nevil
11) Ain't My Fault - Olympia Brass Band
12) Iko Iko - Dixie Cups
13) Hey Pocky - nay - Meters
14) They All Ask For You - Meters
15) Mardi Gras In New Orleans - Dirty Dozen Brass Band
16) Tipitina - Professor Longhair
17) Ain't there no more - Benny Grunch Bunch
18) Mardi Gras Medley - Mardi Gras Big Shots
19) Mardi Gras in Mobile - Ray Parnell
20) Project Love - Rebirth Brass Band
21) Fire on the Bayou - The Neville Brothers
22) Bourbon Street Parade
23) Mardi Gras City - Olympia Brass Band
24) South Rampart Street Parade
25) Walking to New Orleans - Fats Domino
26) Handa Wanda Part 1 - Bo Dollis Wild Magnolias Indians
27) Handa Wanda Part 2 - Bo Dollis Wild Magnolias Indians
28) New Second Line - Olympia Brass Band
29) If Ever I Cease To Love - A.J. Loria
30) Tiger Rag - Olympia Brass Band
31) Just A Closer Walk With Thee
32) Ain't No Place To Pee On Mardi Gras Day - Benny Grunch
33) Fire Water - The Wild Magnolias
34) Olympia On Parade - Olympia Brass Band
35) Dat's Mardi Gras - Jake The Snake
36) Jockomo - Sugarboy Crawford
37) Olympia Special - Olympia Brass Band
38) Lil' Liza Jane - Dirty Dozen Brass Band
39) The Day After Mardi Gras - The Lakefront Loungers
40) Mardi Gras Mambo - The Hawketts

Rank is determined by airplay on WWOZ radio, KMEZ radio, and records sales as provided by LA Music factory, Odyssey Records and reviews by Mardi Gras Digest and Offbeat Magzines.

-snip-

Unfortunately, only a few of these songs have hyperlinks to some information about the recordings and the song's lyrics.

But still, much thanks to Mardi Gras Digest for this list.