JQuery UI Autocomplete from Coffeescript

Your syntax is indeed wrong. The main issue with it is indentation. Blocks are defined with indentation in CoffeeScript, so you probably wanted something like this:

$( '#searchbar' ).autocomplete
  source: ( request, response ) ->
    $.ajax({
      url: "$$ apiUrl pt.casemanagement $$/case/search"
      success: ( data ) ->
        response([
          { label: "Example", value: 'Testing'}
        ])
    })

Also, you were closing the options object to the $.ajax call before finishing the literal object definition. I didn't change any other whitespace or syntax to make it clear what the indentation implies.

In CoffeeScript, you can omit parens for function calls with arguments and braces around objects (unless it's ambiguous or you need to bypass the default precedence rules), so your code would look cleaner like this:

$('#searchbar').autocomplete
  source: (request, response) ->
    $.ajax
      url: "$$ apiUrl pt.casemanagement $$/case/search"
      success: (data) ->
        response [
          label: 'Example'
          value: 'Testing'
        ]

If you need further details about why and how this works, let me know and I can go line-by-line over it.

Sidenote: you're not using the request parameter to get the autocomplete values from the server. That means you probably won't get the expected results from the server, since you're not sending it the search term.