How can I add an autocorrect mapping to the iOS dictionary?
My workaround has been to add a keyboard shortcut that replaces the text ill with I'll any time I add it. Not perfect, but as a stop-gap it will do.

To add the shortcut go to Settings -> General -> Keyboard and scroll to the bottom of the page. You will see an Add New Shortcut... button. Press it.



In the Shortcut configuration page type I'll in to the Phrase entry box and ill in to the Shortcut entry box and press the Save button.



Now any time you type ill it will auto-correct to I'll.