As has been stated elsewhere, in a Capybara test you typically want to do POSTs by submitting a form just like the user would.

The Capybara Ruby gem doesn’t support POST requests, the built-in visit method always uses GET. This is by design and with good reason: Capybara is built for acceptance testing and a user would never ask to ‘post’ parameter X and Y to the application. There will always be some kind of interface, a form for example. It makes more sense to simulate what the visitor would really do

Some of these are absent-by-design