According to the documentation at https://asana.com/developers/api-reference/stories, I should be able to create a Story for either a Task or a Project.
POST /tasks/task-id/stories
POST /projects/project-id/stories
However, I'm having no luck adding stories to projects. The error message is pretty straightforward, "Cannot comment on this object". It would appear that there is no way to do this in the web UI either. Does this just mean that the API documentation is incorrect?
curl -u $ASANA_API_KEY: https://app.asana.com/api/1.0/tasks/4646321361313/stories -d "text=This is a comment"
--- RESPONSE ---
{"data":{"id":4646330012437,"created_at":"2013-03-22T20:23:45.645Z","source":"api","type":"comment","text":"This is a comment","created_by":{"id":1071358442997,"name":"Chris LoPresto"},"target":{"id":4646321361313,"name":"Here is a task"}}}
curl -u $ASANA_API_KEY: https://app.asana.com/api/1.0/projects/4646342124006/stories -d "text=This is a comment"
--- RESPONSE ---
{"errors":[{"message":"target: Cannot comment on this object"}]}
I assume that the documentation was wrong when you posted this, and has been fixed in the year since.
In the Stories section of the API doc, it says:
Stories are a form of history in the system, and such they are read-only.
It also says about the story target attribute:
target - read-only. The object this story is associated with. Currently may only be a task.