I agree with Jeff, as long as you are willing to spray, as he is.
I haven't seen evidence of immunity to Mango Bacterial Black Spot by any mango variety.
Florigon and Duncan are very tough, but I have seen a couple of infected fruits on both. Glenn and Cogshall seem pretty good also.
Po Pyu Kalay, Nam Doc Mai, Elephant Tusk, Lemon Zest; and Kent, Southern Blush, Cushman, all seem very susceptible.