I have seen cases such as yours and the posts were covered with a vinyl sleeve and cap. I haven't used these myself, but it appears that the sleeve is dropped down from the top and held in place with the cap.
How about this? http://www.certainteed.com/products/fence-railing-deck/railing/313642
How about this? http://www.certainteed.com/products/fence-railing-deck/railing/313642
