My current burners are rusted badly. Is there a material that will not rust or more slowly? We live near the coast and high humidity

At this time, there is not any other material version of these burners. We can look into sourcing them in Cast Stainless, but this summer (2019) we only have the cast iron. You can try 'sealing' your burners in interims where you're not cooking often: brush them off with a stainless steel bristled brush and then rub some oil into the surface of the burners. This is a similar process you would use for a cast iron pan. It won't protect them forever in high humidity, but it should help some.