Anchor bag
I think that in the most recent edition of Good Old Boat magazine, there was an article about a similar situation regarding not having anywhere to stow the anchor line. The author of the article had a "canvas" bag made that hung off the pulpit and served the need. Since reading the article, I have started keeping my rode in a canvas bag on the pulpit. It works OK, but it is a temporary measure until I can get something more permanent built.