Ascorbic acid is said to help, many natural Antibiotics will help. Eradicating pylori is hard, but ascorbic acid by example is known to reduce it a lot (taken at least 4-5 times a day).
Some say that Bismuth can eradicate it if used for a certain period (I forgot how long). You can find "Milk of Bismuth" or its more commercial and less healthy version, Pepto Bismol. Using too much bismuth for too long is bad for the liver.