we used paint on some wood chairs recently and they got moldy after rain
Most exterior latex house paint should work.
Spray with wet & forget outdoor. It has some type of inhibitor that will help to prevent this type of issue. But as Ken said, you should use exterior paint. Unfortunately, they don't have an inhibitor in them but I believe Sherwin Williams will add one - they will for interior paint.
It's an absolute must to prime the wood with Kilz before painting. Latex exterior or marine grade paint after the Kilz has dried